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### Section 3.6 : Derivatives of Exponential and Logarithm Functions

For problems 1 – 6 differentiate the given function.

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