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

Question

↳Redirected from "How do I change #int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2)xydzdydx# to cylindrical or spherical coordinates?"

8947 views around the world

You can reuse this answer
Creative Commons License

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)#