trkshspo

2023-03-11

What is the derivative of ${e}^{x\mathrm{ln}2}$?

Nhluvukoj6m

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

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