Question

Find f '(x) for f(x) = 2x3 - 4x2 + 6x - 25

Answer 1

Do you know what to do first?

Answer 2

no

Answer 3

Plug it into that same formula I gave you:

\[f'(x) = \lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h}\]and grind through the algebra

Answer 4

Okay so first, I will give you the equation for figuring out derivatives: \[f'(x) = \lim_{h \rightarrow 0}\frac{ f(x+h)- f(x) }{ h }\]

Answer 5

Get it right this way and I'll teach you the shortcut method. :)

Answer 6

as an example, I'll do \(f(x) = 2x+3\)

\[f'(x) = \lim_{h\rightarrow 0}\frac{(2(x+h)+3) - (2(x)+3)}{h}\]\[=\lim_{h\rightarrow 0}\frac{(2x+2h+3) - (2x+3)}{h} = \lim_{h\rightarrow 0}\frac{2x+2h+3 - 2x-3}{h} \]\[=\lim_{h\rightarrow 0}\frac{2h}{h} = 2\]

Answer 7

ok thanks i got f '(x) = 6x^2 - 8x - 19

Answer 8

Where'd that 19 come from? Remember that the derivative of a constant, such as of -25, is zero (0).

Answer 9

oh opps f '(x) = 6x^2 - 8x + 6

Answer 10

A lot better! :)

Answer 11

perfect :)

Answer 12

remember : \(\rm If~y=x^n~then~y'=n \cdot~x^{n-1}\)

Answer 13

The method used here involves several rules of differentiation:
1. The constant coefficient rule
2. The power rule (given by secret88, above)
3. The addition and subtraction rules for differentiation

Note that it's also possible to obtain the derivative using the definition of the derivative.

Answer 14

thanks :)

Answer 15

I assumed (perhaps incorrectly) that as your previous question involved the definition of the derivative, this one was expected to be done that way instead of by the power rule. Power rule certainly involves less algebra to do!