Question

Use the definition of the derivative to find the derivative of f(x)=6

Answer 1

zero

Answer 2

0

Answer 3

Totally zero

Answer 4

rate of a constant =0

Answer 5

How do I know its zero? how do you find that?

Answer 6

becuase the derivative of any constant is 0 ...like 6 or 7 or 5000000

Answer 7

what if F(x)=2x^3-1

Answer 8

6x^2

Answer 9

how do u know that?

Answer 10

you need to calculate:
\[\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}\]
knowing that:\[f(x)=6\] so \[f(x+h)=6\]

Answer 11

that is the definition of a derivative.

Answer 12

brought the exponent down and multiplied it to the coefficient then subtracted the exponent by one

Answer 13

it seems like the poster is just learning the rules of the derivative, so posting rules that we all know about derivatives isnt what he/she is looking for.

Answer 14

yes ive just started learning derivatives

Answer 15

Since f(x) = 6, is the constant function, f(anything) = 6. So when calculating the limit we obtain:
\[\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\rightarrow 0}\frac{6-6}{h}=\lim_{h\rightarrow 0}\frac{0}{h}=0\]

Answer 16

You need to do it from first principals
lim(f(x+h) -f(x))/h as h --> 0
lim(6 - 6)/h
= 0/h
= 0
fx = 6
f(x+h) = 6

Answer 17

thank you!

Answer 18

if it was f(x) = x +6
it would be
lim((x +h +6) - x +6)/h
lim(h/h)
= 1