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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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