# Differentiate $f(x)=\int_{\sqrt{x}}^{\arcsin x} \ln\theta d \theta$

## Answer

\[(\int_{g(x)}^{h(x)}f(\theta)d\theta)'=h'(x)f(h(x))-g'(x)f(g(x)).\]

Using this formula we get

\[f'(x)=(\arcsin x)' \ln(\arcsin x)-(x^{1/2})'\ln(x^{1/2})\]

\[=\frac{1}{\sqrt{1-x^2}} \ln(\arcsin x)-\frac{1}{2}x^{-1/2}\ln (x^{1/2}).\]

Erdos

4.7K

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.

- answered
- 1569 views
- $2.00

### Related Questions

- How do you go about solving this question?
- Calculus - Derivatives (help with finding a geocache)
- Epsilon-delta definitoon of continuity for $f : x → x^3$
- Solve this problem using branch and bound algorithm.
- Center of algebra of functions
- Can we use the delta-ep def of a limit to find a limiting value?
- Calculus Question
- Linearly independent vector subsets.