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Find the derivative of the function. y = \int_{cos \space x}^{sin \space x} ln(2+7v) dv

Question:

Find the derivative of the function.

{eq}y = \int_{cos \space x}^{sin \space x} ln(2+7v) {/eq} dv

Leibniz Integral Rule:

In calculus, Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, states that for an integral of the form: {eq}\int\limits_{a(x)}^{b(x)} {f(x,v)dv} {/eq},

then the derivative of this integral is expressible as:

{eq}\frac{d}{{dx}}\int\limits_{a(x)}^{b(x)} {f(x,v)dv} = f(x,b(x))\frac{d}{{dx}}b(x) - f(x,a(x))\frac{d}{{dx}}a(x) + \int\limits_{a(x)}^{b(x)} {\frac{\partial }{{\partial x}}} f(x,v)dv {/eq}

Answer and Explanation:

Here we have to find: {eq}\frac{d}{{dx}}\int_{\cos x}^{\sin x} l n(2 + 7v) dv {/eq}

By using Leibniz integral rule, we can say:

{eq}\frac{d}{{dx}}\...

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Gottfried Leibniz: Biography & Contributions to Math

from Calculus: Homework Help Resource

Chapter 13 / Lesson 6
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