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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.

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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