Implicit Differentiation

Implicit Differentiation - Trigonometric Functions


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

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

If sin(x+3y)=y4cosx,\sin (x+3y)=y^{4}\cos x, what is dydx?\frac{dy}{dx}?

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

If x2y2+xsiny=13,x^2y^2+x\sin y=13, what is dydx?\displaystyle \frac{dy}{dx}?


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