Question

If f(x) = (x-1)^3/2 + e^x-2/2, then f^1(2)

Answer 1

what is the meaning of ^1?
Is that the fist derivative?

Answer 2

\[f \prime (2)\]

Answer 3

Ok, so it is to mean the first derivative.
Thanks.
So which part are you having trouble finding the derivative of?
The first term or the second term?

Answer 4

for the first term you can find the derivative of it by using a combination of the chain rule and product rule:
\[[(f(x))^n ]'=n[f(x)]^{n-1} \cdot f'(x)\]
for the second term you can find the derivative of it using the derivative of e^x is e^x and the chain rule and the constant rule:
\[[\frac{e^{f(x)}}{c}]'=\frac{f'(x)e^{f(x)}}{c}\]

Answer 5

constant multiple rule*

Answer 6

And correct me if I'm wrong but I'm reading it as:
\[f(x)=(x-1)^\frac{3}{2}+\frac{e^{x-2}}{2} \]

Answer 7

yes that is correct