How do you use the product rule to find the derivative of $y=x^2*sin(x)$ ?

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Answer 1 · 2018-03-23T04:13:13

$y'=x(2sinx+xcosx)$

The Product Rule tells us that if we have two functions $f(x), g(x),$ multiplied by one another, then

$(fg)'=fg'+gf'$

Here, for $y=x^2sinx,$ we see $f(x)=x^2, g(x)=sinx$

Thus,

$y'=sinxd/dxx^2+x^2d/dxsinx$

$y'=2xsinx+x^2cosx$

Factor out $x$ to simplify:

$y'=x(2sinx+xcosx)$

How do you use the product rule to find the derivative of y=x^2*sin(x)y=x^2*sin(x) ?