# Help with Differentiating

• Jan 28th 2010, 04:27 PM
wopashui
Help with Differentiating
F (x) = $\displaystyle 5^{-2x^2+x}$
• Jan 28th 2010, 04:33 PM
drumist
The general rule for a constant raised to a function of x is:

if $\displaystyle f(x)=a^{g(x)}$ then

$\displaystyle f'(x) = g'(x) \cdot \ln(a) \cdot a^{g(x)}$

Can you apply the rule?
• Jan 28th 2010, 04:34 PM
General
Quote:

Originally Posted by wopashui
F (x) = $\displaystyle 5^{-2x^2+x}$

Just apply the following:
If $\displaystyle f(x)=a^{g(x)}$ where $\displaystyle a>0$.
then: $\displaystyle f'(x)=a^{g(x)} g'(x) ln(a)$.
• Jan 30th 2010, 11:43 AM
wopashui
Quote:

Originally Posted by General
Just apply the following:
If $\displaystyle f(x)=a^{g(x)}$ where $\displaystyle a>0$.
then: $\displaystyle f'(x)=a^{g(x)} g'(x) ln(a)$.

can you explain what F (x) is, it's not the same as f (x), isn't it?
• Jan 30th 2010, 01:19 PM
Defunkt
Quote:

Originally Posted by wopashui
can you explain what F (x) is, it's not the same as f (x), isn't it?

It is exactly the same. We could also write the function as $\displaystyle \phi (x), \epsilon (x), \mu (x), g(x), G(x), u(x), V(x)$ etc etc...