# Find y'. Do not simplify.{eq}y = x^5 cot^{-1} x + cos^{-1} (7x + 2) {/eq}

## Question:

Find y'. Do not simplify.{eq}y = x^5 cot^{-1} x + cos^{-1} (7x + 2) {/eq}

## Application of product rule and chain rule in differentiation:

Differential calculus is used to find the derivative of a function with respect to a variable. The given function is a complicated function and it requires both chain rule and product rule. The formula for product rule is {eq}(uv)'=uv'+vu' {/eq}. The formula for chain rule is : {eq}\displaystyle \frac{d}{dx} f(g(x))=f'(g(x))\frac{d}{dx} g(x) {/eq}.

Other formulae used in this problem are:

{eq}\begin{align*} \int x^a dx&=\frac{x^{a+1}}{a+1}\\ \int \cot^{-1}x\ dx&=\frac{-1}{1+x^2}\\ \int \cos^{-1}x\ dx&=\frac{-1}{\sqrt{1-x^2}} \end{align*} {/eq}

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{eq}\begin{align*} y&=x^5 \cot^{-1} x + \cos^{-1} (7x + 2)\\ y'&=x^5\left ( \frac{-1}{1+x^2} \right )+(\cot^{-1}... Differential Calculus: Definition & Applications

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Chapter 13 / Lesson 6
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This lesson explores differential calculus. It defines a differential and delves into the many uses of differential equations.