Question

Derivative of the square root of (x) times sinx

Answer 1

You are finding the derivative of the square root of a product:

y = sqrt ( x * sin x ) = ( x * sin x )^(1/2) This is a power function!

Apply the Power Rule with Chain Rule. This involves two main steps:

1. Find the derivative of ( x * sin x)^(1/2) with respect to (x * sin x). This is

(1/2) (x * sin x)^(-1/2).

2. Multiply this result by the derivative of x * sin x (which is a PRODUCT).

Can you finish this? Hint: You must now apply the product rule.

Answer 2

d/dx * sqrt(x) * sin(x) =
`d/dx √(x)*sin(x) + d/dx*sin(x) √(x)`
=
`(1)/(2 √(x)) * sin(x) + cos(x)* √(x)`
=
`(sin(x)+2xcos(x))/(2 √(x))`