Solving: $\frac{d}{dx}\left(y=\ln\left(\arccos\left(x\right)\right)\right)$
Exercise
$\frac{dy}{dx}\left(y=\ln\left(\cos^{-1}\left(x\right)\right)\right)$
Step-by-step Solution
Learn how to solve differential calculus problems step by step online. Find the implicit derivative d/dx(y=ln(arccos(x))). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Taking the derivative of arccosine.
Find the implicit derivative d/dx(y=ln(arccos(x)))
Final answer to the exercise
$y^{\prime}=\frac{-1}{\sqrt{1-x^2}\arccos\left(x\right)}$