How do you differentiate f(x)= e^(2x)* (x^2 - 4) *ln xf(x)=e2x⋅(x2−4)⋅lnx using the product rule?

1 Answer
Jim G.
Jan 5, 2017

f'(x)=e^(2x)[lnx(x^2-4)+2xlnx+1/x(x^2-4)]

Explanation:

#To differentiate the product of 3 functions

(abc)'=a'bc+b'ac+c'ab

rArra=e^(2x)rArra'=e^(2x).d/dx(2x)=2e^(2x)

b=x^2-4rArrb'=2x

"and " c=lnxrArrc'=1/x

rArrf'(x)=2e^(2x)(lnx(x^2-4))+2x(e^(2x)lnx)+1/x(e^(2x)(x^2-4))

=e^(2x)[lnx(x^2-4)+2xlnx+1/x(x^2-4)]

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