### Home > APCALC > Chapter 7 > Lesson 7.3.2 > Problem7-114

7-114.

Differentiate each of the following equations.

1. $f(x) =\frac { \operatorname { tan } ( x ) } { e ^ { - x } }$

You could use the Quotient Rule, or rewrite this fraction without the negative exponent in the denominator.

1. $y^3 - 3xy = 3^y$

$\frac{d}{dx}(y^{3}-3xy)=\frac{d}{dx}(3^{y})$

$y'=\frac{-3y}{\ln(3)\cdot e^{y}+3x-3y^{2}}=\frac{dy}{dx}$

1. $g(t) = \ln(t)\sqrt { t }$

Before differentiating, rewrite $g(t)$ with a fractional exponent.