Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
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 \(\displaystyle V\left( t \right) = \frac{t}{{{{\bf{e}}^t}}}\) is increasing or decreasing at the following points.
- \(t = - 4\)
- \(t = 0\)
- \(t = 10\)
- Determine if \(G\left( z \right) = \left( {z - 6} \right)\ln \left( z \right)\) is increasing or decreasing at the following points.
- \(z = 1\)
- \(z = 5\)
- \(z = 20\)