Question

How do you differentiate `y=5x^3(sinx)^2`?

Answer 1

`dy/dx=5x^3sin2x+15x^2sin^2x`

Explanation:

`"differentiate using the "color(blue)"product rule"`

`"given "y=g(x).h(x)" then "`

`dy/dx=g(x)h'(x)+h(x)g'(x)larr" product rule"`

`g(x)=5x^3rArrg'(x)=15x^2`

`h(x)=(sinx)^2rArrh'(x)=2sinxcosx=sin2x`

`rArrdy/dx=5x^3sin2x+15x^2sin^2x`