Quiz 4. Implicit Differentiation + Slope of the Tangent Line

Find dy/dx  if     12x + 4y = 10

•  $\frac{dy}{dx}=-\frac{1}{3}$  

•  $\frac{dy}{dx}=-\frac{1x}{3y}$  

•  $\frac{dy}{dx}=-3$  

•  $\frac{dy}{dx}=\frac{1}{3}$  

Find dy/dx if      $3x^2-6y^3=13$  

•  $\frac{dy}{dx}=\frac{x}{3y^2}$  

•  $\frac{dy}{dx}=-\frac{x}{3y^2}$  

•  $\frac{dy}{dx}=\frac{18x}{6y^2}$  

•  $\frac{dy}{dx}=-\frac{3x}{y^2}$  

Differentiate w.r.t x,

 $-4x^2+12x+6y^2-10y=5$  

•  $\frac{dy}{dx}=\frac{2\left(2x-3\right)}{6y-5}$  

•  $\frac{dy}{dx}=\frac{-2\left(2x-3\right)}{6y-5}$  

•  $\frac{dy}{dx}=\frac{\left(2x-3\right)}{6y-5}$  

•  $\frac{dy}{dx}=\frac{-8x+12}{12y-10}$  

•  $\frac{dy}{dx}=\frac{-8x+12}{6y-5}$  

Find dy/dx if        $3x^2+6y^2+10=5x+7y+100$  

•  $\frac{dy}{dx}=\frac{-6x+5}{12y-7}$  

•  $\frac{dy}{dx}=\frac{-6x+5}{-12y+7}$  

•  $\frac{dy}{dx}=\frac{6x-5}{12y-7}$  

•  $\frac{dy}{dx}=\frac{-3x+5}{6y-7}$  

•  $\frac{dy}{dx}=\frac{3x-5}{6y-7}$  

What is dy/dx if

 $2x^7y^4=10$  

•  $\frac{dy}{dx}=-\frac{7y}{4x}$  

•  $\frac{dy}{dx}=-\frac{7x}{4y}$  

•  $\frac{dy}{dx}=-\frac{4x}{7y}$  

•  $\frac{dy}{dx}=-\frac{14y}{4x}$  

•  $\frac{dy}{dx}=\frac{7y}{4x}$  

Find dy/dx if

 $5x^3+2x^4y^2=10$  

•  $\frac{dy}{dx}=\frac{-8x^3y^2-15x^2}{4x^4y}$  

•  $\frac{dy}{dx}=\frac{8x^3y^2+15x^2}{4x^4y}$  

•  $\frac{dy}{dx}=\frac{16x^3y^2-15x^2}{4x^4y}$  

•  $\frac{dy}{dx}=-\frac{4x^2y}{8xy^2+15}$  

Find dy/dx if 8xy = 12

• $\frac{dy}{dx}=-\frac{y}{x}$

• $\frac{dy}{dx}=\frac{y}{x}$

• $\frac{dy}{dx}=-\frac{x}{y}$

• $\frac{dy}{dx}=\frac{x}{y}$

 $-3\sin x+4\cos y=10$  

Differentiate w.r.t x 

•  $\frac{dy}{dx}=-\frac{3\cos\left(x\right)}{4\sin\left(y\right)}$  

•  $\frac{dy}{dx}=\frac{3\cos\left(x\right)}{4\sin\left(y\right)}$  

•  $\frac{dy}{dx}=-\frac{3\cos\left(y\right)}{4\sin\left(x\right)}$  

•  $\frac{dy}{dx}=\frac{3\cos\left(y\right)}{4\sin\left(x\right)}$  

Find dy/dx if    $8\sin y+11\cos x=13$  

•  $\frac{dy}{dx}=\frac{11\sin\left(x\right)}{8\cos\left(y\right)}$  

•  $\frac{dy}{dx}=-\frac{11\sin\left(x\right)}{8\cos\left(y\right)}$  

•  $\frac{dy}{dx}=-\frac{11\cos\left(x\right)}{8\sin\left(y\right)}$  

•  $\frac{dy}{dx}=\frac{11\sin\left(y\right)}{8\cos\left(x\right)}$  

Find dy/dx if     $13\cos x+2\sin y=14$  

•  $\frac{dy}{dx}=\frac{13\sin x}{2\cos y}$  

•  $\frac{dy}{dx}=-\frac{13\sin x}{2\cos y}$  

•  $\frac{dy}{dx}=\frac{13\cos x}{2\sin y}$  

•  $\frac{dy}{dx}=-\frac{13\cos x}{2\sin y}$  

•  $\frac{dy}{dx}=\frac{13\sin y}{y\cos x}$