Question

What is the derivative of `5x arcsin(x)`?

Answer 1

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

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)=5xrArrg'(x)=5`

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

`rArrd/dx(5xarcsinx)`

`=5x xx1/sqrt(1-x^2)+arcsinx xx5`

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