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If #f(x)= cos3x # and #g(x) = sqrt(x+3 #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer

Feb 25, 2016

#(d(f@g)(x))/dx=-3/(2sqrt(x+3))sin(3sqrt(x+3))#

Explanation:

The composition function #(f@g)(x)# is found as follows :

#f[g(x)]=f(sqrt(x+3))#

#=cos(3sqrt(x+3))#

#therefore(d(f@g)(x))/dx=d/dxcos(3sqrt(x+3))#

#=-sin(3sqrt(x+3))*3/2(x+3)^(-1/2)(1)#

#=-3/(2sqrt(x+3))sin(3sqrt(x+3))#

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