Question

A student is asked to find the derivative of y = x sin2 (x) with respect to variable x, given x, y > 0. They provide the following answer: dy dx = sin2 (x) · x sin2 (x)−1 · cos2 (x) Is the student correct? If the student is correct, then explain how they used derivative rules correctly to find this derivative. If the student is incorrect, then give the correct answer and provide an explanation that you would use to correct the student’s thinking.

Answer 1

Answer:

$\frac{dy}{dx} = 2x ( 2cos2x) +sin2x$

$\frac{dy}{dx} = 4x( cos2x)+sin2x$

Step-by-step explanation:

Given y = x sin2x .....(1)

Applying UV formula $\frac{d(UV)}{dx} = u \frac{dv}{dx} + v\frac{du}{dx}$

Differentiating with respective to 'x' we get

$\frac{dy}{dx} = x ( 2cos2x)\frac{d(2x)}{dx} +sin2x (1)$

$\frac{dy}{dx} = x ( 2cos2x)(2) +sin2x (1)$

Final answer:-

$\frac{dy}{dx} = 4x( cos2x)+sin2x$