How do you differentiate #(2^x)x^2#?

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Answer 1 · 2016-03-19T16:43:57

The derivative is # x 2^x(2+x ln2 )#

Use #a^x=e^(x ln a)#.

The function is #e^(x ln 2)x^2#.

Apply product rule for differentiation.

The derivative is

#ln2e^(x ln2)x^2 + e^(x ln 2)2x#

= #xe^(x ln 2)(2+x ln 2)#

= # x 2^x(2+x ln2 )#