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: 1

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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

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Chapter 13 / Lesson 6
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In this lesson, we will explore the life and work of German mathematician and philosopher, Gottfried Wilhelm von Leibniz. In particular, we'll identify his major contributions to the field of mathematics, published books and technological accomplishments.


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