What is the Rule for Finding Derivatives of Exponential Functions?

[Ry122]

Hi
Can someone please tell me what the name of the method used to find the derivative of eponential functions is? eg. e^.5x the derivative is .5e^.5x
Can you also give me the rule. eg. dy/dx=du/dv x dy/dx

 

[cristo]

1. I'm not sure that it has a name-- it's just the derivative of the exponential function!

2. I don't know what you mean. Could you expand a little?

 

[neutrino]

I have not heard of any 'named' method specifically for finding the derivatives of exponential functions, but I think what you maybe looking for is the Chain Rule.

Can you also give me the rule. eg. dy/dx=du/dv x dy/dx

?

 

[nicktacik]

\frac{d}{dx} e^{f(x)}=\frac{df}{dx}e^{f(x)}

 

[EnumaElish]

In general, d(a^x)/dx = Log(a) a^x.

Let f(x) = a^x, then Log(f(x)) = x Log(a). Differentiating, f'(x)/f(x) = Log(a) or f'(x) = Log(a) f(x).