Question

What is the derivative of `f(x)=cossqrt(x)`?

Answer 1

`d/dx cos(sqrt(x)) = -sin(sqrt(x))/(2sqrt(x))`

Explanation:

Applying the chain rule, together with the derivatives

• `d/dx cos(x) = -sin(x)`

• `d/dx sqrt(x) = 1/(2sqrt(x))`

we get

`d/dx cos(sqrt(x)) = -sin(sqrt(x))(d/dx sqrt(x))`

`= -sin(sqrt(x))(1/(2sqrt(x)))`

`= -sin(sqrt(x))/(2sqrt(x))`