Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 13

$2^{x^{2}}\cdot x\cdot \ln 2$

$\quad$ $\displaystyle \frac{d}{dx}[b^{u}]=b^{u}\ln b\cdot\frac{du}{dx}$ $b=2$ $u(x)=x^{2}-1\displaystyle \qquad \frac{du}{dx}=2x$ $\displaystyle \frac{d}{dx}[b^{x^{2}-1}]=2^{x^{2}-1}\ln 2\cdot 2x$ $=2^{x^{2}-1+1}\cdot x\cdot\ln 2=2^{x^{2}}x\ln 2$