find the derivative

**dat1611** · July 30th 2009, 09:29 AM

h'(x)=

**Plato** · July 30th 2009, 09:51 AM

$H(x) = \int_c^{f(x)} {G(t)dt} \, \Rightarrow \,H'(x) = G\left( {f(x)} \right)f'(x)$

**dat1611** · July 30th 2009, 10:12 AM

i cant get it could use some more help

**skeeter** · July 30th 2009, 10:31 AM

Originally Posted by dat1611

i cant get it could use some more help

$\frac{d}{dx}\left[\int_a^u f(t) \, dt \right] = f(u) \cdot \frac{du}{dx}$

substitute $u = \sin{x}$ in for $t$ in the integrand, then multiply that result by the derivative of $\sin{x}$ .

**Twig** · July 30th 2009, 10:52 AM

Hi!

Let $u = sin(x)$

$h(u)=\int_{-5}^{u} (cos(t^{3})+t) \; dt$

$\frac{dh}{dx}=\frac{dh}{du} \cdot \frac{du}{dx}$

$h'(x)=(cos(sin^{3}(x))+sin(x))\cdot cos(x)$

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