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Step-by-step Solution

Find the derivative using the product rule $\frac{d}{dx}\left(5x\arccos\left(7x^5\right)\right)$

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(5x\cdot arccos\left(7x^5\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$5\frac{d}{dx}\left(x\arccos\left(7x^5\right)\right)$

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(5x*arccos(7*x^5)). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\arccos\left(7x^5\right). The derivative of the linear function is equal to 1. Taking the derivative of arccosine.

Answer

$5\arccos\left(7x^5\right)+\frac{-175x^{5}}{\sqrt{1-49x^{10}}}$

Problem Analysis