Question

Use the definition of the derivative to find the derivative of each function with respect to x.
f(x)=x^2 - x - 5
Can anyone explain how to do it?

Answer 1

Do you knw the power rule?

Answer 2

\[\large
\frac{d}{dx}x^n = nx^{n-1} \\ \large
f(x) = x^2 - x - 5 \\ \large
f'(x) = \frac{d}{dx}x^2 - \frac{d}{dx}x - \frac{d}{dx}5 = ?
\]

Answer 3

The power rule lets use x^2

Answer 4

\[x ^{2}= 2x.........3x^3 = 9x^2.........x ^{-4 }=-4x ^{-5}\]

Answer 5

In the power rule to find the derivative you take the \[x ^{n}=n x ^{n-1}\]

Answer 6

Do you see this?

Answer 7

Yes Thank you!

Answer 8

Ok so for your equation you need the derivative for each value

Answer 9

\[
\large
\frac{d}{dx}x^n = nx^{n-1} \\ \large
f(x) = x^2 - x - 5 \\ \large
\frac{d}{dx}f(x) = \frac{d}{dx}x^2 - \frac{d}{dx}x - \frac{d}{dx}5 \\ \large
\frac{d}{dx}f(x) =~~~2x~~~ -~~~~ 1 ~~~- ~~~~0 \\ \large
\frac{d}{dx}f(x) = 2x - 1
\]