Calculus
Implicit Differentiation
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 \(\displaystyle \frac{dy}{dx}?\)