$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $x ^ { 4 } + 7 x + 6 x y - y ^ { 7 } = 9$
A)$\frac { d y } { d x } = - \frac { 4 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$
B)$\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 - 6 y } { 7 y ^ { 6 } - 6 x }$
C)$\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 + 6 y } { 6 y ^ { 6 } - 6 x }$
D)$\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$
E)$\frac { d y } { d x } = \frac { 3 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$

Question

Quizplus · Accepted Answer

We differentiate both sides of the equation with respect to x, using the chain rule on the y-term:
$$4x^3+6x\frac{dy}{dx}+6y+6x\frac{d}{dx}(y)-7y^6\frac{dy}{dx}=0$$
Simplifying and solving for $\frac{dy}{dx}$, we get
$$\frac{dy}{dx}=\frac{4x^3+7+6y}{7y^6-6x}$$
Therefore, the answer is (D).

Find dydx by implicit differentiation. \text { Find } \frac { d y } { d x } \text { by implicit differentiation. } Find dxdy​ by implicit differentiation.

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$