Answered: "What is the derivative of x 2 ..."

College
Calculus and Analysis
Differential Calculus
Derivatives

jistefaftexia99kq6

Answered question

2022-05-07

What is the derivative of

x^{2} ﻿ \ln (x)

Answer & Explanation

Raelynn Parker

Beginner2022-05-08Added 12 answers

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = x^{2}$ and $g (x) = \ln (x)$ .

$x^{2} \frac{d}{d x} [\ln (x)] + \ln (x) \frac{d}{d x} [x^{2}]$

The derivative of $\ln (x)$ with respect to $x$ is $\frac{1}{x}$ .

$x^{2} \frac{1}{x} + \ln (x) \frac{d}{d x} [x^{2}]$

Differentiate using the Power Rule.

$2 x \ln (x) + x$

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