Question

3. Find the derivative of ƒ(x) = x^2 + 5^x using the definition of a derivative (first principles).

Answer 1

what's your answer here?

Answer 2

here's a hint
\[\frac{d}{dx} a^x = a^x \ln a\]

Answer 3

I know the answer is 2x +5^x (log(5) through using the various derivative rules
However, i dont know how I can show the log(5) part through first principles

Answer 4

it's implicit differentiation

Answer 5

have you discussed that lesson?

Answer 6

No sir

Answer 7

oh wait...definition as in limits?

Answer 8

Yes first principles h->o (F(X+h)-f(x)/h

Answer 9

uhmm maybe @zepp is more suitable for this job...

Answer 10

sorry not good with limits..he is though...just wait for @zepp

Answer 11

alright will do
Im guessing by linking him he will be informed of this question existing? :p

Answer 12

Simply plug in the function and solve the limit? Where's the problem?

Answer 13

How do you make it so that you get 5^x(log5)?
I cant figure that out

Answer 14

Yep that's right

Answer 15

that's the derivative of 5^x

Answer 16

\[\large \frac{d}{dx}x^2=2x\] Cheating by using the fact that \(\huge \frac{d}{dx}x^n=nx^{(n-1)}\)

Answer 17

Ive found it so that lim (h-0) is equal to 5^x(5^h-1)/h
But how would I continue that?
And I know thats the derivative, I just cant find the answer using first principles

Answer 18

So \[\large f(x)=x^2 + 5^x \\\large \frac{d}{dx}x^2 + 5^x=2x+5^x{\log(5)}\]

Answer 19

5xlog(5) <------ How would I show that using first principles? For this specific question I cannot use any derivation rules

Answer 20

@Zarkon Any suggestion on deriving a function that consists of a constant raised to the x power?

Answer 21

Using the first principals?