Dereiv. of 4^x + 3^x + 9^-x

1. Nov 9, 2004

EvilPony

if anyone can teach me how to do this that would be great, thanks.

dereiv. means derivative sorry

2. Nov 9, 2004

stunner5000pt

when im doing something with the form something raised to x i always remember - keep the tern , log (or ln, same meaning here) the base number

and then differentiate the exponent

for example for $$\frac{d}{dx} (3^x) = 3^x Log3 (1)$$

as you can see keep the function 3^x, log the base Log3, and then differentiate teh numerator (1).

3. Nov 9, 2004

Zurtex

All I can say to the above post, is eh? That would mean that it would be 0. In general:

$$\frac{d}{dx} \left( a^x \right) = \ln (a) \; a^x$$

Where a is some constant. Here is the method used to work it out and generally useful for this type of problem:

$$y= a^x$$

$$\ln y = \ln \left( a^x \right)$$

$$\ln y = x \ln a$$

$$\frac{dy}{dx} \frac{1}{y} = \ln a$$

$$\frac{dy}{dx} = (\ln a)y$$

$$\frac{d}{dx} \left( a^x \right) = \ln (a) \; a^x$$

4. Nov 9, 2004

stunner5000pt

what would be zero??