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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.

# Trigonometric Functions

If $$10xy=\cot(xy),$$ what is $$\displaystyle \frac{dy}{dx}?$$

If $$7\cos x \sin y=11,$$ what is $$\displaystyle \frac{dy}{dx}?$$

If $$\sin (x+3y)=y^{4}\cos x,$$ what is $$\frac{dy}{dx}?$$

Let $$y = \sin(6x + 20y)$$. The slope of the tangent at the point $$(x,y) = (0,0)$$ can be expressed as $$-\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

If $$x^2y^2+x\sin y=13,$$ what is $$\displaystyle \frac{dy}{dx}?$$

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