Question

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

Answer 1

The derivative is `ln(2)e^(x*ln(2))=ln(2)e^(ln(2^(x)))=ln(2)2^(x)`

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`.