Question

What is the derivative of the F(x)=3e^2? e is the natural log base = 2.7128. Please show the steps.

Answer 1

3e^2 is a constant. The derivative of a constant is 0.

Answer 2

or did you mean f(x) = 3e^x?

Answer 3

Yes

Answer 4

Do you want me to take the derivative via the limit of the difference quotient?

Answer 5

Sure. thanks

Answer 6

\[f'(x) = \lim_{h \rightarrow 0} \frac {f(x+h)-f(x)}{h}\]\[f(x) = 3e^x\]\[f'(x) = \lim_{h \rightarrow 0} \frac {3e^{x+h} - 3e^x}{h}\]\[f'(x) = \lim_{h \rightarrow 0} \frac {3e^x(e^h - 1)}{h} = f'(x) = \lim_{h \rightarrow 0} 3 e^x \times \frac {(e^h - 1)}{h} = 3e^x * 1 = 3e^x\]

Answer 7

Another known limit is used in taking this derivative by the way.\[\lim_{h \rightarrow 0} \frac {a^h - 1}{h} = \ln a\]In that case,\[\lim_{h \rightarrow 0} \frac {e^h - 1}{h} = \ln e = 1\]

Answer 8

This is great! Thank you! My computation had gotten to 0 * 2.7128x * (0.9980).

Answer 9

Your welcome =)