# 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??