Question

How do you find the derivative of `(x^2)(sinx)(tanx)`?

Answer 1

`2xsinxtanx+x^2cosxtanx+x^2sinxsec^2x`

Explanation:

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

`"the rule for differentiating the product of 3 functions is"`

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

`dy/dx=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)`

`f(x)=x^2rArrf'(x)=2x`

`g(x)=sinxrArrg'(x)=cosx`

`h(x)=tanxrArrh'(x)=sec^2x`

`"hence derivative"`

`=2xsinxtanx+x^2cosxtanx+x^2sinxsec^2x`