Question

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Answer 1

thanks!!!

Answer 2

The first question seems a bit trivial... any function's derivative can be found using the chain rule, even one as simple as \(f(x)=x\).

Answer 3

As for the second question, the units of the independent variable do not matter. False.

Answer 4

For (d), find the derivative of each function and compare the two.

Answer 5

(e) should be pretty clear.

Answer 6

life saver! thanks a bunch! e is true?

Answer 7

Yes. Given any positive base \(a\), you have
\[\frac{d}{dx}a^x=\frac{d}{dx}e^{\ln a^x}=\frac{d}{dx}e^{x\ln a}=\ln a~e^{x\ln a}=\ln a~a^x\]
which is the original function multiplied by the logarithm of the base. (Notice that when \(a=e\), you get \(\dfrac{d}{dx}e^x=e^x\)).

Answer 8

Even if \(a=1\), I'd argue that \(\ln 1~1^x\) is still technically an exponential function, but I'm sure there's some caveat in the definition of an exponential function that says it has to be non-zero.

Answer 9

thanks again, is c true? and d false?