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

Question

myininaya · Answer

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

anonymous · Answer

$$f \prime (2)$$

myininaya · Answer

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?

myininaya · Answer

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:
$$[\frac{e^{f(x)}}{c}]'=\frac{f'(x)e^{f(x)}}{c}$$

myininaya · Answer

constant multiple rule*

myininaya · Answer

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

anonymous · Answer

yes that is correct