Find $y ^ { \prime }$ implicitly for $8 x ^ { 9 } - y ^ { 9 } = 5$
A) $y ^ { \prime } = \frac { 8 x ^ { 9 } } { y ^ { 9 } }$
B) $y ^ { \prime } = \frac { y ^ { 9 } } { 8 x ^ { 9 } }$
C) $y ^ { \prime } = \frac { 8 x ^ { 8 } } { y ^ { 8 } }$
D) $y ^ { \prime } = \frac { y ^ { 8 } } { 8 x ^ { 8 } }$
E) $y ^ { \prime } = \frac { x ^ { 8 } } { 8 y ^ { 8 } }$

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation $8x^9 - y^9 = 5$ with respect to $x$ gives $72x^8 - 9y^8y' = 0$. Solving for $y'$ yields $y' = \frac{72x^8}{9y^8} = \frac{8x^8}{y^8}$.

Find y′y ^ { \prime }y′ Implicitly For 8x9−y9=58 x ^ { 9 } - y ^ { 9 } = 58x9−y9=5

Find $y ^ { \prime }$ Implicitly For $8 x ^ { 9 } - y ^ { 9 } = 5$