How to differentiate e^(2x)=sin(x+3y)?

Question

#e^(2x)#=sin(x+3y)

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Answer 1 · 2016-02-23T17:14:21

You can do it like this:

#e^2x=sin(x+3y)#

Take the derivative with respect to #x# of both sides implicitly:

#D[e^2x]=D[sin(x+3y)]#

#:.2e^2x=cos(x+3y).d((x+3y))/dx#

#:.2e^2x=cos(x+3y)(1+3(dy)/(dx))#

#:.(2e^2x)/(cos(x+3y))=1+3(dy)/(dx)#

#:.3(dy)/(dx)=(2e^2x)/(cos(x+3y))-1#

#:.dy/dx=(2e^2x)/(3cos(x+3y))-1/3#