If #f(x) =-e^(-3x-7) # and #g(x) = lnx^2 #, what is #f'(g(x)) #?

1 Answer
P dilip_k
Jul 28, 2017

If #f(x) =-e^(-3x-7) # and #g(x) = lnx^2 #, what is #f'(g(x)) #?

Given

#f(x) =-e^(-3x-7) #

Differentiating w . r to x we gat

#f'(x) =-e^(-3x-7)xx(d/(dx) (-3x-7)) #

#=>f'(x) =3e^(-3x-7) #

Inserting #x=g(x)# we have

#f'(g(x)) =3e^(-3g(x)-7) #

#=>f'(g(x)) =3e^-7xxe^(-3g(x)) #

#=>f'(g(x)) =3e^-7xxe^(-3 lnx^2) #

#=>f'(g(x)) =3e^-7xxe^( lnx^(2*(-3)) #

#=>f'(g(x)) =3e^-7xxe^( lnx^(-6)) #

#=>f'(g(x)) =3e^-7xxx^(-6) #

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