Calculus

# Implicit Differentiation - Inverse Trigonometric Functions

If $\displaystyle \tan^{-1} \left(x^2y\right)=3x+6y,$ what is $\frac{dy}{dx} ?$

Given the function $\tan^{-1}(4xy)=5,$ What is $\frac{dy}{dx}?$

If $\displaystyle \cos^{-1} \left(\frac{6x-y}{3x+y}\right)=e^a,$ what is $\frac{dy}{dx} ?$

If $\displaystyle \sin^{-1} (7x^2-y^2)=\ln 6,$ what is $\frac{dy}{dx} ?$

Given the function $\cos^{-1}(3x+11y)=12,$ what is $\frac{dy}{dx} ?$

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