Question

If $y^3+x^3+3xy=15$, then $\frac{dy}{dx}$ at $(1,2)$ is equal to

• A. $\frac{3}{5}$
• B. $\frac{-3}{5}$
• C. $\frac{5}{3}$
• D. $\frac{-5}{3}$

Answer 1

Answer: (B)

$3y^2{y}^{\prime }+3x^2+3\left(x{y}^{\prime }+y\right)=0\Rightarrow 4y^{\prime }+1+1y^{\prime }+2=0\Rightarrow y^{\prime }=\frac{-3}{5}$