What are the derivatives of logarithmic functions?

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What are the derivatives of logarithmic functions?

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Answer 1 · 2014-10-21T19:47:37

The derivative of a logarithmic function is (1/the function)*derivative of the function.

For example, $\frac{d}{d x} log x = \frac{1}{x}$ $d/dx log x= 1/x$

Consider another example.

$\frac{d}{d x} log (1 + x^{3}) = \frac{1}{1 + x^{3}} 3 x^{2}$ $d/dx log (1+ x^3)= 1/ (1+x^3) 3x^2$

In the first example, the function was x. Thus, derivative of the log function was 1/the function *derivative of the function, i.e. , $\frac{1}{x} \cdot 1$ $1/x *1$

In the second example, the function was $1 + x^{3}$ $1+x^3$ . It's derivative is $3 x^{2}$ $3x^2$ . Hence derivative of the log function was $\frac{1}{1 + x^{3}} 3 x^{2}$ $1/ (1+x^3) 3x^2$ .

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What are the derivatives of logarithmic functions?

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