Pre-Video Questions

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Before watching the videos, think about and answer these questions to the best of your ability.

Compute the derivative to each of the following functions:

If $f(x) = \dfrac {e^x}{x^3}$ , then $f'(x) =$

$\dfrac {3x^2}{e^x}$ $\dfrac {e^x*3x^2-x^3e^x}{x^6}$ $\dfrac {e^x}{3x^2}$ $\dfrac {x^3e^x-e^x*3x^2}{x^6}$ $\dfrac {x^3e^x+e^x*3x^2}{x^6}$

If $f(x) = \dfrac {\sin (x)}{3^x}$ , then $f'(x) =$

$\dfrac {3^x\cos (x)-\sin (x)3^x\ln (3)}{9^x}$ $\dfrac {3^x\cos (x)+\sin (x)3^x\ln (3)}{9^x}$ $\dfrac {\cos (x)}{3^x\ln (3)}$ $\dfrac {3^x\cos (x)-\sin (x)3^x\ln (3)}{3^x}$ $\dfrac {3^x\ln (3)}{\cos (x)}$

If $f(x) = \dfrac {\ln (x)}{2x^2}$ , then $f'(x) =$

$\dfrac {4x-4x\ln (x)}{2x^2}$ $4x^2$ $\dfrac {x-2\ln (x)x}{2x^4}$ $\dfrac {4x+4x\ln (x)}{2x^2}$ $\dfrac {1}{4x^2}$