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Math Help - differentiation question 2

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    differentiation question 2

    derivate \int_{sin(x)}^{0} \frac{dt}{\sqrt{1-t^2}},

    |x|< \frac{\pi}{2}
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    Quote Originally Posted by peteryellow View Post
    derivate \int_{sin(x)}^{0} \frac{dt}{\sqrt{1-t^2}},

    |x|< \frac{\pi}{2}
    \int_{sin(x)}^{0} \frac{dt}{\sqrt{1-t^2}} = -\int_0^{sin(x)} \frac{dt}{\sqrt{1-t^2}}

    \frac{d}{dx}\left[-\int_0^{sin(x)} \frac{dt}{\sqrt{1-t^2}} \right]= -\frac{1}{1-\sin^2{x}} \cdot \cos{x} = -\sec{x}
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