# Finding derivative of function

• November 17th 2012, 03:26 PM
johnsy123
Finding derivative of function
How would i find the derivative of:

y=integral from x to sqrt{x} of costheta/theta.

Does this involve the quiotient rule? i get confused with how to evaluate these when it's in the form of an integral, some clarity would be great thanks.
• November 17th 2012, 03:29 PM
Re: Finding derivative of function
Recall the Fundamental Theorem of Calculus
• November 17th 2012, 03:39 PM
Plato
Re: Finding derivative of function
Quote:

Originally Posted by johnsy123
How would i find the derivative of:
y=integral from x to sqrt{x} of costheta/theta.

Is it $y = \int_x^{\sqrt x } {\frac{{\cos (\theta )}}{\theta }d\theta } ~?$
If each of $f~\&~g$ is a differentiable function and $y = \int_{g(x)}^{f(x)} {h(\theta )d\theta }$ then $y' = h(f(x))f'(x) - h(g(x))g'(x)$