How do you differentiate $log ({sin}^{2} (x))$ $log(sin^2(x))$ ?

Question

21442 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-10T00:42:45

$2 cot (x)$ $2cot(x)$

This answer assumes that $log (x) = {log}_{e} (x)$ $log(x)=log_e(x)$ , the natural logarithm.

First use the rule $log (a^{b}) = b log (a)$ $log(a^b)=blog(a)$ :

$y = log ({sin}^{2} (x)) = 2 log (sin (x))$ $y=log(sin^2(x))=2log(sin(x))$

From here, we need to know that $\frac{d}{d x} log (x) = \frac{1}{x}$ $d/dxlog(x)=1/x$ . Through the chain rule, $d/dxlog(f(x))=1/f(x)*f'(x)$ .

Then:

$dy/dx=2(1/sin(x))(d/dxsin(x))=2/sin(x)(cos(x))=2cot(x)$

How do you differentiate log(sin^2(x))log(sin2(x))log(sin^2(x))?