Question

How do you find the derivative of `f(x)=5x arcsin(x)`?

Answer 1

`f'(x)=(5x)/(sqrt(1-x^2))+5arcsinx`

Explanation:

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

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

`f'(x)=g(x)h'(x)+h(x)g'(x)larr" product rule"`

`g(x)=5xrArrg'(x)=5`

`h(x)=arcsinxrArrh'(x)=1/(sqrt(1-x^2))`

`rArrf'(x)=(5x)/(sqrt(1-x^2))+5arcsinx`