Find $y ^ { \prime }$ when $4 x \sin y + 5 y \ln x = 11$
A) $\frac { - ( 4 x \sin y + 5 y ) } { x ( 4 x \cos y + 5 \ln x ) }$
B) $\frac { - ( 4 x \sin y + y ) } { x ( 4 x \sin y + 5 \ln x ) }$
C) $\frac { - ( 4 x \cos y + 5 ) } { ( 4 y \cos y + 5 x ) }$
D) $\frac { - ( 5 x \sin y + 4 y ) } { ( 4 x \cos y + 5 \ln x ) }$

Question

Quizplus · Accepted Answer

To find $y'$, we differentiate both sides of the equation $4x\sin y + 5y\ln x = 11$ with respect to $x$, using implicit differentiation. Differentiating the left side gives $4\cos y \cdot y' + 4\sin y + \frac{5y}{x} + 5\ln x \cdot y'$. The right side, being a constant, differentiates to 0. Solving for $y'$ gives the expression in choice A.

Find y′y ^ { \prime }y′ When 4xsin⁡y+5yln⁡x=114 x \sin y + 5 y \ln x = 114xsiny+5ylnx=11

Find $y ^ { \prime }$ When $4 x \sin y + 5 y \ln x = 11$