$\dfrac{d}{dx}{\, \cos^{-1}{x}} \,=\, -\dfrac{1}{\sqrt{1-x^2}}$

When $x$ represents a variable, the inverse cosine function is written as $\cos^{-1}{(x)}$ or $\arccos{(x)}$ in inverse trigonometry. In differential calculus, the derivative of the cos inverse function with respect to $x$ is written in following two mathematical forms.

$(1) \,\,\,$ $\dfrac{d}{dx}{\, \Big(\cos^{-1}{(x)}\Big)}$

$(2) \,\,\,$ $\dfrac{d}{dx}{\, \Big(\arccos{(x)}\Big)}$

The derivative of the inverse cos function with respect to $x$ is equal to the negative reciprocal of the square root of the subtraction of square of $x$ from one.

$\implies$ $\dfrac{d}{dx}{\,\Big(\cos^{-1}{(x)}\Big)}$ $\,=\,$ $-\dfrac{1}{\sqrt{1-x^2}}$

The differentiation of the cos inverse function can be written in any variable. Here are few examples to learn how to write the formula for the derivative of cosine inverse function in differential calculus.

$(1) \,\,\,$ $\dfrac{d}{dz}{\,\Big(\cos^{-1}{(z)}\Big)}$ $\,=\,$ $-\dfrac{1}{\sqrt{1-z^2}}$

$(2) \,\,\,$ $\dfrac{d}{du}{\,\Big(\cos^{-1}{(u)}\Big)}$ $\,=\,$ $-\dfrac{1}{\sqrt{1-u^2}}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\,\Big(\cos^{-1}{(y)}\Big)}$ $\,=\,$ $-\dfrac{1}{\sqrt{1-y^2}}$

Learn how to prove the differentiation of the inverse cosine function formula by first principle.

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved