If $x ^ { 6 } + y ^ { 6 } = - 27$ , what is $\frac { d y } { d x }$ ?
A) $- \frac { 27 + x ^ { 5 } } { y ^ { 5 } }$
B) $- \frac { x ^ { 5 } } { y ^ { 5 } }$
C) $x ^ { 5 } - y ^ { 5 }$
D) $- \frac { 6 x ^ { 5 } } { y ^ { 5 } }$

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation $x^6 + y^6 = -27$ with respect to $x$, we get $6x^5 + 6y^5 \frac{dy}{dx} = 0$. Solving for $\frac{dy}{dx}$, we get $\frac{dy}{dx} = -\frac{x^5}{y^5}$.

If x6+y6=−27x ^ { 6 } + y ^ { 6 } = - 27x6+y6=−27

If $x ^ { 6 } + y ^ { 6 } = - 27$