Question

I have the anser can someone check me please.
Find the derivative of the following. m is a constant.
f(x)=4x^2m

Answer 1

The answer I got is 8x^m

Answer 2

Is the original problem \[\Large f(x) = 4x^{2m}\]

Answer 3

yes

Answer 4

ok so you would bring down the exponent, then multiply it with the coefficient 4 to get 8m

that's the new coefficient

Answer 5

then you would subtract 1 from 2m to get 2m-1

that's the new exponent

Answer 6

so

\[\Large f(x) = 4x^{2m}\]


\[\Large f^{\prime}(x) = 8mx^{2m-1}\]

Answer 7

oh ok why does the m come down next to the 8 if it was a n exponent before.

Answer 8

because in general, the power rule is this

if

\[\Large f(x) = x^{n}\]

then

\[\Large f^{\prime}(x) = n*x^{n-1}\]

Answer 9

the 2m is part of the exponent, so in effect, n = 2m

Answer 10

oh ok thanks

Answer 11

you're welcome