Mathematics
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OpenStudy (anonymous):
What am I doing wrong?
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OpenStudy (anonymous):
f(x) = 6x + 2 at x = 1
6(1)^2+2
8
but it's not one of my choices
OpenStudy (anonymous):
Finding the derivative
hartnn (hartnn):
finding the derivative of f(x) = 6x+2 at x=1
is this your question ?
whats f(x) exactly ?
OpenStudy (anonymous):
yes that's it
OpenStudy (anonymous):
f(x)=6x+2
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hartnn (hartnn):
whats the derivative of 6x
whats the derivative of 2
?
OpenStudy (anonymous):
I don't understand
hartnn (hartnn):
f(x) = 6x+2
whats the derivative of f(x) ?
f'(x) = ...
OpenStudy (anonymous):
1
hartnn (hartnn):
not actually
derivative of constant = 0
so derivative of 2 is 0
for 6x,
d/dx (6x) = 6 d/dx (x) = 6
so f'(x) = 6
makes sense ?
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OpenStudy (anonymous):
kind of
OpenStudy (anonymous):
Is the derivative of every constant 0?
hartnn (hartnn):
so f'(x) = 6
at every point, including x=1
and yes
derivative of every constant =0
OpenStudy (anonymous):
Ohh because you did 6(1)+0 right?
hartnn (hartnn):
yes
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OpenStudy (anonymous):
and is that like the formula to find derivatives?
OpenStudy (anonymous):
d/dx (6x) = 6 d/dx (x) = 6 This one
OpenStudy (anonymous):
do i have to do that ^ can't i just replace the 2 with a zero and the x with a 1?
hartnn (hartnn):
\(\Large \dfrac{d}{dx}x^n = n x^{n-1}\)
^^ thats the general formula
hartnn (hartnn):
constants can be taken out of derivative
so
d/dx (6x) = 6 d/dx(x)
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OpenStudy (anonymous):
how would i use that?
hartnn (hartnn):
and according to that formula
d/dx(x) = 1
hartnn (hartnn):
you just replace 'n' by the exponent of x
OpenStudy (anonymous):
so in this case the x would be one?
hartnn (hartnn):
example :
if i need derivative of x^6
we replace n by 6
d/dx(x^6) = 6 x^5
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hartnn (hartnn):
n would be 1
OpenStudy (anonymous):
yes i meant the n
OpenStudy (anonymous):
okay it makes a bit more sense thanks for your help :)
hartnn (hartnn):
welcome ^_^