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Derivative of Logarithmic Functions Calculator

Get detailed solutions to your math problems with our Derivative of Logarithmic Functions step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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Example

Solved Problems

Difficult Problems

1

Here, we show you a step-by-step solved example of derivative of logarithmic functions. This solution was automatically generated by our smart calculator:

$\frac{d}{dx}\left(x\ln\left(x\right)\right)$
2

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\ln\left(x\right)$

$\frac{d}{dx}\left(x\right)\ln\left(x\right)+x\frac{d}{dx}\left(\ln\left(x\right)\right)$
3

The derivative of the linear function is equal to $1$

$\ln\left(x\right)+x\frac{d}{dx}\left(\ln\left(x\right)\right)$
4

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\ln\left(x\right)+x\frac{1}{x}$

Multiply the fraction by the term $x$

$\ln\left(x\right)+\frac{1x}{x}$

Any expression multiplied by $1$ is equal to itself

$\ln\left(x\right)+\frac{x}{x}$

Simplify the fraction $\frac{x}{x}$ by $x$

$\ln\left(x\right)+1$
5

Multiply the fraction by the term $x$

$\ln\left(x\right)+1$

Final answer to the problem

$\ln\left(x\right)+1$

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