Differentiating e^x

[kenhung123]

So when we differentiate functions in the form does it mean because of the chain rule?
where
Does it mean the derivative of exponentials are always itself but because of the chain rule, we may have a term to multiply?

[Aqualim]

In General;


in this case


Now this works with the original aswell cause we know the derivative of becomes 1 so basically you are just multiplying by 1 which leaves it as it is.

So for the question you have above you first find the derivative of then you just place it out the front of . Which becomes;

[tcg93]

So when we differentiate functions in the form does it mean because of the chain rule?
where
Does it mean the derivative of exponentials are always itself but because of the chain rule, we may have a term to multiply?

Yep. Pretty much. I just remember it as
(Derivative of the power) x
where in this case the Derivative of the Power is 1.

[tcg93]

So when we differentiate functions in the form does it mean because of the chain rule?
where
Does it mean the derivative of exponentials are always itself but because of the chain rule, we may have a term to multiply?

Yep. Pretty much. I just remember it as
(Derivative of the power) x
where in this case the Derivative of the Power is 1.

Note that is just for exponentials, not polynomials

[TyErd]

So when we differentiate functions in the form does it mean because of the chain rule?
where
Does it mean the derivative of exponentials are always itself but because of the chain rule, we may have a term to multiply?

Yep. Pretty much. I just remember it as
(Derivative of the power) x
where in this case the Derivative of the Power is 1.

I also do it that way but Im just wondering would I lose marks in the exams because usually my answers are one liners with no working out.

[Ilovemathsmeth]

I absolutely love differentiation.

Okay, that said.

Another common trap people fall into is differentiating exponentials of other bases. Keep in mind that the above formula of (derivative of u) only works for base e. If you've got base 10, or 2 or whatever, you HAVE to use the change of base rule to make it base e, and THEN you can apply the above rule. This came up on a SAC once and a LOT of people got it wrong

[the.watchman]

Another common trap people fall into is differentiating exponentials of other bases. Keep in mind that the above formula of (derivative of u) only works for base e. If you've got base 10, or 2 or whatever, you HAVE to use the change of base rule to make it base e, and THEN you can apply the above rule. This came up on a SAC once and a LOT of people got it wrong

Oh, and might I add that the same applies to logs, where
This only works for base e, and so for other bases, use the change base formula

[kenhung123]

Could you give an example?

[tcg93]

Could you give an example?

=

Now is a constant

Therefore the derivative is

[the.watchman]

Ok:





(loge(2) is a constant)





Try an exponential one yourself

[kenhung123]

Hmm??? Sorry won't constants dissapear?

[the.watchman]

Only when they're by themselves: like x^2+1 => 2x

But in this scenario(as a coefficient), it's like kx^2 => 2kx (if you know what I mean)

[stonecold]

This thread is going to help with my SAC coming up on Thursday.  Thanks.

[Ilovemathsmeth]

Exactly. Please use change of base rule for logarithms to differentiate; this came up on a SAC and there were a LOT of people who incorrectly differentiated and lost marks as a result.