Question

Problem C4 Due in 21 hours, 30 minutes Find the first and second derivatives with respect to x of exp(/a)-exp(-xa) 2 where exp(x)-e is the exponential function. Enter your answer in terms of the exponential function df/ dx= Submit Answer Tries 0/10 Submit Answer Tries 0/10

Answer 1

Formula

$\frac{d}{dx} \left [ e^{\frac{x}{a}} \right ]=\frac{1}{a}e^{\frac{x}{a}}$

$\frac{d}{dx} \left [ e^{-\frac{x}{a}} \right ]=\frac{-1}{a}e^{\frac{x}{a}}$

a)

$\frac{df}{dx} =\frac{\frac{1}{a}e^{\frac{x}{a}}-\left ( \frac{-1}{a}e^{\frac{-x}{a}} \right )}{2}$

$\frac{df}{dx} =\frac{e^{\frac{x}{a}}+e^{-\frac{x}{a}}}{2a}$

b)

$\frac{d^{2}f}{dx^{2}} =\frac{\frac{1}{a}e^{\frac{x}{a}}+\left ( -\frac{1}{a} \right )e^{-\frac{x}{a}}}{2a}$

$\frac{d^{2}f}{dx^{2}} =\frac{e^{\frac{x}{a}}-e^{-\frac{x}{a}}}{2a^{2}}$