Question

find fourth derivative of x³ log x​

Answer 1

Step-by-step explanation:

this question's answer is 6/x

Answer 2

The fourth derivative of  $x^3log x$ is $-\frac{1}{x^2}$.

Given,

The expression, $x^3log x$.

To Find,

The fourth derivative of  $x^3log x$.

Solution,

We can solve the mathematical derivative problem using the following method.

The formula to find the derivative is as follows,

• The derivative of $x^n$ with respect to x is $x^{n-1}$ .
• The derivative of $log x$ with respect to x is, $\frac{1}{x}$.

• The first derivative of (f(x)+g(x)) with respect to x is f'(x)g(x)+f(x)g'(x).

The first derivative of $x^3log x$ is,

$\frac{d}{dx} (x^3logx)$

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

=$\frac{d}{dx} (x^2logx+x^2 )$

The second derivative of $x^3log x$ is,

=$=\frac{d}{dx} (x^1logx+x^2.\frac{1}{x} +x^1 )$

$\frac{d}{dx} (xlogx+2x )$

The third derivative of $x^3log x$ is,

$\frac{d}{dx} (logx+x.\frac{1}{x} +2)$

=$\frac{d}{dx} (logx+3 )$

The fourth derivative is,

=$\frac{d}{dx} (\frac{1}{x} +0 )$

=$\frac{d}{dx}(x^{-1})$

=$-\frac{1}{x^2}$.

Hence, The fourth derivative of  $x^3log x$ is $-\frac{1}{x^2}$.

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