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

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

May 21, 2023

May 16, 2023

May 10, 2023

May 03, 2023

Latest Math Problems

May 09, 2023

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

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

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved