How to solve for dy/dx? #tany=e^x +lnx#

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#tany=e^x +lnx#

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Answer 1 · 2018-02-14T03:26:22

#dy/dx=(xe^x+1)/(xsec^2y)#

Differentiate both sides implicitly w.r.t #x#

#tany=e^x+lnx#

#sec^2y*dy/dx=e^x+1/x#

Divide both sides by #sec^2y#

#dy/dx=(e^x+1/x)/sec^2y#

Simplify:

#dy/dx=e^x/sec^2y+1/(xsec^2y)#

#dy/dx=(xe^x+1)/(xsec^2y)#