Question

Find the derivative of f(x)=x^3+4x-2 using the derivative formula

Answer 1

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Answer 2

f'=3x^2 +4

Answer 3

Well, use the difference quotient which is:
\[\lim_{h \rightarrow 0}\frac{f(x)-f(x+h)}{h}\].
So:
\[\lim_{h \rightarrow 0}\frac{(x^3+4x-2)-((x+h)^3+4(x+h)-2)}{h}\].
Then simplify.

Answer 4

Or maybe you meant:
\[\frac{d}{dx}(x^n)=nx^{n-1}\].
Whoops lol. If so, disregard above^^. (even though it works)

Answer 5

d/dx (f(x))=f'(x)=lim h->0 f(x+h)=f(x) / h
f(x) = x^3 + 4x - 2
f(x+h)+ (x+h)^3 + 4(x+h) - 2
x^3 +3x^2h+3xh^2+h^3+4x+4h-2

d/dx (x^3+4x-2) = lim h-> 0 (x^3+3x^2h+3xh^2+h^3+4x+4h-2)-(x^3+4x-2) / h

= lim h->0 3x^2h + 3xh^2 + h^3 + 4h / h

= lim h-> 0 3x^2 + 3xh + 4
= 3x^2+4