The answer is ##cos^2(x)-sin^2(x)+2cos(x)sin(x)=cos(2x)+sin(2x)##
First, use the to say
##d/dx(sin(x)(sin(x)+cos(x)))=cos(x)(sin(x)+cos(x))+sin(x)(cos(x)-sin(x))##
Next, expand this out to write
##d/dx(sin(x)(sin(x)+cos(x)))=cos^2(x)-sin^2(x)+2cos(x)sin(x)##
Finally, use the double-angle formulas ##cos^2(x)-sin^2(x)=cos(2x)## and ##2cos(x)sin(x)=sin(2x)## to write
##d/dx(sin(x)(sin(x)+cos(x)))=cos(2x)+sin(2x)##
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Get The Answer What is the derivative of ##sinx(sinx+cosx)##?
The answer is ##cos^2(x)-sin^2(x)+2cos(x)sin(x)=cos(2x)+sin(2x)##
First, use the to say
##d/dx(sin(x)(sin(x)+cos(x)))=cos(x)(sin(x)+cos(x))+sin(x)(cos(x)-sin(x))##
Next, expand this out to write
##d/dx(sin(x)(sin(x)+cos(x)))=cos^2(x)-sin^2(x)+2cos(x)sin(x)##
Finally, use the double-angle formulas ##cos^2(x)-sin^2(x)=cos(2x)## and ##2cos(x)sin(x)=sin(2x)## to write
##d/dx(sin(x)(sin(x)+cos(x)))=cos(2x)+sin(2x)##
Previous answers to this question
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