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# Implicit Differentiation

Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.

# 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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