Exercises

01

Derivative rules

Differentiate these functions, citing the appropriate derivative rules:

• $f(x)=(3x^2-5x)e^x$
• $h(t)=(1-e^t)(t+e^t)$

02

Derivative rules

Assume that $f(4)=2$ and $f^{\prime }(4)=6$ and $g(4)=5$ and $g^{\prime }(4)=-3$.

Apply the derivative rules and use the data above to find $h^{\prime }(4)$:

• (a) $h(x)=f(x)g(x)$
• (b) $h(x)=\frac{f(x)}{g(x)}$
• (c) $h(x)=\frac{g(x)}{f(x)+g(x)}$

03

Finding lines

There are two lines parallel to the line $x-2y=2$ and tangent to the curve $y=\frac{x-1}{x+1}$. Find both lines.