Implicit Differentiation - Trigonometric Functions Practice Problems Online

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 $\frac{dy}{dx}?$

\frac{y^{4}\sin x+\cos (x+3y)}{y^{4}\cos x-\cos (x+3y)}

\frac{\cos x}{\sin (x+3y)}

\frac{y^{4}\sin x+\cos (x+3y)}{4y^{3}\cos x-3\cos (x+3y)}

\frac{\cos x}{4\sin (x+3y)}

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 $\displaystyle \frac{dy}{dx}?$

\frac{-2xy^2-\sin y}{2x^2y+x\cos y}

\frac{-2xy^2+\sin y}{2x^2y+x\cos y}

\frac{2xy^2-\sin y}{2x^2y+x\cos y}

\frac{2xy^2+\sin y}{2x^2y+x\cos y}

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Implicit Differentiation - Trigonometric Functions