Differentiating Logarithmic Functions without Base e

Key Questions

What is the derivative of $y=log_3(x)$ ?

By Change of Base Formula: $log_bx={log_ax}/{log_ab}$ ,

$y=log_3x={lnx}/{ln3}$

By taking the derivative,

$y'={1/x}/{ln3}=1/{(ln3)x}$

Wataru · 4 · Sep 22 2014
What is the derivative of $f(x)=log_2(cos(x))$ ?

Answer:

$-tan(x)/ln(2)$

Explanation:

$f(x)=log_2(cos(x))=ln(cos(x))/ln(2)$

$1/ln(2)$ is just a constant and can be ignored.

$(ln(u))'=(u')/u$

$u=cos(x), u'=-sin(x)$

$f'(x)=1/ln(2)*(-sin(x))/cos(x)=-tan(x)/ln(2)$

Martin C. · 1 · Mar 18 2018
What is the change of base rule for logarithms?

Change of Base Formula

$log_bx={log_ax}/{log_ab}$ ,

where $a$ is any positive number except $1$ .

I hope that this was helpful.

Wataru · · Oct 16 2014

Questions

What is the derivative of $f(x)=log_b(g(x))$ ?
What is the derivative of $f(x)=log(x^2+x)$ ?
What is the derivative of $f(x)=log_4(e^x+3)$ ?
What is the derivative of $f(x)=x*log_5(x)$ ?
What is the derivative of $f(x)=e^(4x)*log(1-x)$ ?
What is the derivative of $f(x)=log(x)/x$ ?
What is the derivative of $f(x)=log_2(cos(x))$ ?
What is the derivative of $f(x)=log_11(tan(x))$ ?
What is the derivative of $f(x)=sqrt(1+log_3(x)$ ?
What is the derivative of $f(x)=(log_6(x))^2$ ?
What is the derivative of $f(x)=sin(log_2(x))$ ?
What is the derivative of $y=log_10(x)$ ?
What is the derivative of $y=log_2(x)$ ?
What is the derivative of $y=log_3(x)$ ?
What is the change of base rule for logarithms?
How do you use logarithmic differentiation to find the derivative of the function?
How do you differentiate $y=(sinx)^(x)$ ?
What is the derivative of $lnx^3$ ?
What is the domain of the derivative of $ln x$ ?
What is the derivative of the $sqrt ln x$ ?
How do you find the derivative of $3x^(lnx)$ ?
What is the derivative of log(x)?
How do you differentiate $f(x)=log_3(xe^x)$ ?
How do you find the derivative of $log_2 (x)$ ?
What is the derivative of $log_3x$ ?
What is the derivative of $y = log (x^2 + 1)$ ?
What is the derivative of $y=(x/e^x)LnX$ ?
What is the derivative of $y=log_x 2$ ?
What is the derivative of $y=log_x 3$ ?
What is the derivative of $y=log_4 2x$ ?
What is the derivative of $log(8x-1)$ ?
What is the derivative of $y = log3 [(x+1/x-1)^ln3]$ ?
What is the derivative of $log_4^(x^2)$ ?
What is the derivative of $log(sin^2(x))$ ?
What is the derivative of $f(x)=log (x/5)$ ?
What is the derivative of $y=(x^2lnx)^4$ ?
What is the derivative of $y=ln sqrt(x+1)^5/sqrt(x+2)^20$ ?
What is the derivative of $y=ln(cos^2ɵ)$ ?
What is the derivative of $ln y=e^y sinx$ ?
What is the derivative of $y=5^sqrt(s)$ ?
What is the derivative of $y=2^(s^2)$ ?
What is the derivative of $y=(sinx)^x$ ?
What is the derivative of $y = ln ((x^2+1)^5 / sqrt(1-x))$ ?
What is the derivative of $log_2(3x-1)$ ?
What is the derivative of $y=1/log_2(x)$ ?
What is the derivative of $y = log_2 (x^4sinx)$ ?
What is the derivative of $g(u) = ln(sqrt((3u+6)/(3u-6)))$ ?
What is the derivative of $ln[sqrt((2+x^2)/(2-x^2))]$ ?
What is the derivative of $y= log (6x-2)$ ?
How do you differentiate $log_2(x^2sinx)$ ?
How do you differentiate $log_2(x^2sinx^2)$ ?
How do you differentiate $log_3(9x^2sin(9x^2) )$ ?
What is the derivative of $y=log_5x$ ?
What is the derivative of $y=log_10x/x$ ?
How do you find the derivative of $log_(3)x$ ?
How do you find the derivative of $y = log (x^2 + 1)$ ?
How do you find the derivative of $f(x) = log_x (3)$ ?
How do you find the derivative of $f(x) = log_x e$ ?
How do you find the derivative of $f(x) = log_x 2$ ?
How do you find the derivative of $log _ 3 (2x) / x^2$ ?
How do you find the derivative of $f(x)=Log_5(x)$ ?
How do you find the derivative of $log(sin^2(x))$ ?
How do you find the derivative of $log 4^(x^2)$ ?
How do you find the derivative of $5^x log_5 x$ ?
How do you find the derivative of $log(8x-1)$ ?
How do you find the derivative of $e^(x*log(x))$ ?
How do you find the derivative of $ln[sqrt(2+x^2)/(2-x^2)]$ ?
How do you find the derivative of $y=log_4 2x$ ?
How do you find the derivative of $y = log_3 [(x+1/x-1)^ln3]$ ?
How do you find the derivative of $y= log _ 10 x/x$ ?
How do you find the derivative of $logx^2$ ?
How do you find the derivative of $1/logx$ ?
How do you find the derivative of $log_10 x$ ?
How do you find the derivative of $log_7x$ ?
Question #4601b
How do you differentiate $log_(3)x$ ?
How do you differentiate $y = log (x^2 + 1)$ ?
How do you differentiate $f(x)=Log_5(x)$ ?
How do you differentiate $y=(x/e^x)Lnx$ ?
How do you differentiate $y=log_x(2)$ ?
How do you differentiate $y=log x^2$ ?
How do you differentiate $log_3 (2x) / x^2$ ?
How do you differentiate $f(x) = log(log x)$ ?
How do you differentiate $f(x) = log_x (3)$ ?
How do you differentiate $y = Ln(5x)$ ?
How do you differentiate $log 4^(x^2)$ ?
How do you differentiate $log_2(3x-1)$ ?
How do you differentiate $y=(x^2lnx)^4$ ?
How do you differentiate $log(sin^2(x))$ ?
How do you differentiate $y = ln ((x^2+1)^5 / sqrt(1-x))$ ?
How do you differentiate $f(x)=log (x/5)$ ?
How do you differentiate $y = 1 / log_2 x$ ?
How do you differentiate $ln[sqrt(2+x^2)/(2-x^2)]$ ?
How do you differentiate $y =5^x log_5 x$ ?
How do you differentiate $y= log (6x-2)$ ?
How do you differentiate $y= e^((3x)/4)$ ?
How do you differentiate $y= 2x^4 - 2x^3 - 8$ ?
How do you differentiate $y = log_2 (x^4sinx)$ ?
How do you differentiate $y=ln[x/(2x+3)]^(1/2)$ ?
How do you differentiate $log_2 (x)$ ?
How do you differentiate $log_2 (e)$ ?
Question #ea87b
Question #484ea
How do you differentiate $y=log_x2$ ?
How do you differentiate $y= ln sqrt( 6x^2+8)$ ?
How do you differentiate $log(8x-1)$ ?
How do you differentiate $y = log_3 [((x+1)/(x-1))^ln3]$ ?
How do you differentiate $log_xe$ ?
How do you differentiate $y= log _10 x$ ?
How do you differentiate $y= log _3 x$ ?
How do you differentiate $y= log _5 x$ ?
How do you differentiate $y= log _a x$ ?
How do you differentiate $y= log _b x$ ?
What is the derivative of $log_2(x^2/(x-1))$ ?
What is the derivative of $log_3((xsqrt(x-1))/2)$ ?
What is the derivative of $log_5sqrt(x^2-1)$ ?
What is the derivative of $log_10((x^2-1)/x)$ ?
What is the derivative of $10log_4x/x$ ?
What is the derivative of $x^(3/2)log_2sqrt(x+1)$ ?
What is the derivative of $y=2^-x$ ?
What is the derivative of $y=5^(x-2)$ ?
What is the derivative of $y=log_10(2x)$ ?
What is the derivative of $y=x^(2/x)$ ?
What is the derivative of $y=x^(x-1)$ ?
What is the derivative of $y=(x-2)^(x+1)$ ?
What is the derivative of $y=(1+x)^(1/x)$ ?
What is the derivative of $y=(sinx)^(2x)$ ?
What is the derivative of $y=(lnx)^(cosx)$ ?
Question #b26e2
How do you find the derivative of $f(x)=3e^2-7log_10x$ ?
How do you find the derivative of $f(x)=ln(x^3)$ ?
How do you find the derivative of $f(x)=ln(2x^2+1)$ ?
How do you find the derivative of $f(x)=ln(2x^2+1)^5$ ?
How do you find the derivative of $f(x)=ln(x^5(x-2)^3)$ ?
How do you find the derivative of $f(x)=ln(root3(x-1)/(x+1))$ ?
Differentiate $(a^2sin^2x+b^2cos^2x)$ ?
Question #cb13a
Question #a787b
Let $y=[(x^(2x)(x-1)^3)/(3+5x)^4]$ , how do you use logarithmic differentiation to find $dy/dx$ ?
How do you find the derivatives of $y=log_2(3x)$ ?
How do you find the derivatives of $y=log_x(a)$ ?
How do you find the derivatives of $y=(3x-2)/(4x+3)$ by logarithmic differentiation?
How do you find the derivatives of $y=(5x-2)^3(6x+1)^2$ by logarithmic differentiation?
How do you find the derivatives of $y=((x^2+1)sqrt(3x+4))/((2x-3)sqrt(x^2-4))$ by logarithmic differentiation?
How do you find the derivatives of $y=x^(2x)$ by logarithmic differentiation?
How do you find the derivatives of $y=(x-1)^(x^2+1)$ by logarithmic differentiation?
How do you find the derivatives of $y=(sintheta)^tantheta$ by logarithmic differentiation?
How do you find the derivatives of $y=e^(e^x)$ by logarithmic differentiation?
How do you find the derivatives of $y=(2x+1)^e$ by logarithmic differentiation?
How do you find the derivatives of $s=roott(t)$ by logarithmic differentiation?
Question #d3912
What is the derivative of $ln3x$ ?
Differentiate $y=(sin(x))^(log(x))$ ?

Differentiating Logarithmic Functions

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Differentiating Logarithmic Functions without Base e

Key Questions

Answer:

Explanation:

Questions

Differentiating Logarithmic Functions