Chapter 2.5, Problem 1C

a.

To determine

To explain: $\frac{d}{dx}\left(e^{\pi }\right)=0$ is true or false.

b.

To determine

To explain: $\frac{d}{dz}\left(e^z\right)=e^z$ is true or false.

c.

To determine

To explain: $\frac{d}{dx}\left(\frac{1}{x}\right)=\ln x$ is true or false.

d.

To determine

To explain: $\frac{d}{dx}\left(\ln \left|x\right|\right)=\frac{1}{\left|x\right|}$ is true or false.

e.

To determine

To explain: If $f$ is an exponential function, then $f^{\text{'}}$ is a constant multiple of $f$ is true or false.

f.

To determine

To explain: If $f^{\text{'}}$ is a constant multiple of $f$ , then $f$ is an exponential function this statement is true or false.

g.

To determine

To explain: Logarithmic differentiation is required in order to differentiate complicated products and quotients this statement is true or false.

h.

To determine

To explain: Logarithmic differentiation is required in order to differentiate expressions that have a variable in both the base and the exponent this statement is true or false.