How do you find the derivative of x^2 sinx?

1 Answer
Ken C.
May 22, 2016

d/dx(x^2sinx)=2xsinx+x^2cosx

Explanation:

The product rule states that:
d/dx(uv)=u'v+uv'
Where u and v are functions of x.

In x^2sinx, we have two functions: x^2 and sinx. Since they are being multiplied together, we'll need to use the product rule to find the derivative.

Let u=x^2 and v=sinx:
u=x^2->u'=2x
v=sinx->v'=cosx

Making necessary substitutions in the product rule, we have:
(2x)(sinx)+(x^2)(cosx)
=2xsinx+x^2cosx

We can't really simplify this further, so we'll leave it as our final answer.

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