How do you differentiate $(x^2) (sin x)$ ?

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Answer 1 · 2016-07-04T00:57:26

By using the product rule.

Let $f(x) = (x^2)(sinx)$ , then $f(x) = g(x) xx h(x)$ .

The derivative of this function is given by $f'(x) = (g'(x) xx h(x)) + (h'(x) xx g(x))$

The derivative of $g(x)$ or $x^2$ is $g'(x) = 2 xx x^(2 - 1) = 2x$

The derivative of $h(x)$ or $sinx$ is $h'(x) = cosx$ .

Applying the product rule:

$f'(x) = (g'(x) xx h(x)) + (h'(x) xx g(x))$

$f'(x) = (2x(sinx)) + (x^2(cosx))$

$f'(x) = 2xsinx + x^2cosx$

Hence, the derivative of $y = (x^2)(sinx)$ is $y' = 2xsinx + x^2cosx$ .

Hopefully this helps!

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