What is the derivative of e^(xln2)exln2?

1 Answer
Bill K.
Jun 26, 2015

The derivative is ln(2)e^(x*ln(2))=ln(2)e^(ln(2^(x)))=ln(2)2^(x)ln(2)ex⋅ln(2)=ln(2)eln(2x)=ln(2)2x

Explanation:

This can be done either by the Chain Rule (d/dx(f(g(x)))=f'(g(x))*g'(x)) or by recognizing that e^(x*ln(2))=e^(ln(2^(x)))=2^(x) and recalling that d/dx(b^{x})=ln(b)*b^{x} when b>0.

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