Question

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

Answer 1

Using the product rule, which states that for a function `y=f(x)g(x)` its derivative will be `y'=f'(x)g(x)+f(x)g'(x)`,

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