# How do you find dy/dx by implicit differentiation for #1+x = sin(xy^2)#?

##### 1 Answer

May 11, 2018

#### Explanation:

Implicitly differentiate the Left-Hand Side with respect to

#d/(dx)[1+x]=1# by the power rule

The right-hand side is slightly trickier...

#color(white)(l)d/(dx)[sin(x*y^2)]#

#=cos(x*y^2)*d/(dx)[x*y^2]#

#=cos(x*y^2)*(y^2+2x*y*(dy)/(dx))#

by the chain rule along with the cosine rule.

Hence

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