Calculus I - Derivatives of Exponential and Logarithm Functions (Practice Problems)

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Section 3.6 : Derivatives of Exponential and Logarithm Functions

For problems 1 – 6 differentiate the given function.

$f\left( x \right) = 2{{\bf{e}}^x} - {8^x}$ Solution
$g\left( t \right) = 4{\log _3}\left( t \right) - \ln \left( t \right)$ Solution
$R\left( w \right) = {3^w}\log \left( w \right)$ Solution
$y = {z^5} - {{\bf{e}}^z}\ln \left( z \right)$ Solution
$\displaystyle h\left( y \right) = \frac{y}{{1 - {{\bf{e}}^y}}}$ Solution
$\displaystyle f\left( t \right) = \frac{{1 + 5t}}{{\ln \left( t \right)}}$ Solution
Find the tangent line to $f\left( x \right) = {7^x} + 4{{\bf{e}}^x}$ at $x = 0$ . Solution
Find the tangent line to $f\left( x \right) = \ln \left( x \right){\log _2}\left( x \right)$ at $x = 2$ . Solution
Determine if V(t)=tet is increasing or decreasing at the following points.
1. $t = - 4$
2. $t = 0$
3. $t = 10$
Solution
Determine if G(z)=(z−6)ln(z) is increasing or decreasing at the following points.
1. $z = 1$
2. $z = 5$
3. $z = 20$
Solution