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

The derivative is $\ln \left(2\right) {e}^{x \cdot \ln \left(2\right)} = \ln \left(2\right) {e}^{\ln \left({2}^{x}\right)} = \ln \left(2\right) {2}^{x}$
This can be done either by the Chain Rule ($\frac{d}{\mathrm{dx}} \left(f \left(g \left(x\right)\right)\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$) or by recognizing that ${e}^{x \cdot \ln \left(2\right)} = {e}^{\ln \left({2}^{x}\right)} = {2}^{x}$ and recalling that $\frac{d}{\mathrm{dx}} \left({b}^{x}\right) = \ln \left(b\right) \cdot {b}^{x}$ when $b > 0$.