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Answer 1 · 2017-08-04T21:38:41

#cos(x)+sec^2(x)#

Since the derivative of a sum is the sum of the derivatives

#(sin(x)+tan(x))'=(sin(x))'+(tan (x))'#

Also, recall that #(sin(x))'=cos (x)#

And #(cos(x))'=-sin(x)#

Then

#(sin(x)+tan(x))'=cos(x)+(tan(x))'#

Since #tan(x)=(sin(x))/(cos(x))#

Then #(tan(x))'=(cos^2(x)+sin^2(x))/(cos^2(x))# by the quotient rule

And since #sin^2(x)+cos^2(x)=1#

#(tan(x))'=1/(cos^2(x))=sec^2(x)#

Then

#(sin(x)+tan(x))'=cos(x)+sec^2(x)#