Question

what is the derivative of (ln(2))(cos 1/4 - x)

Answer 1

i dont understand why its not a negative number, because the derivative of cos(any x) is -sin(any x)

Answer 2

(ln(2))(cos((1)/(4)-x))

cos((1)/(4)-x)

(d)/(dx) 1/4-x=-1

d/dx =sin((1/(4)-x))

sin(1/(4)-x)

Answer 3

it is not clear to me what this function is

Answer 4

\[\ln(2)\cos(\frac{1}{4}-x)\]?

Answer 5

\[\ln(2)\cos(\frac{1}{4-x})\]?

Answer 6

no.... (ln(2))(cos( (1/4) -x ) // i dont understand y its not a negative number

Answer 7

it is a function, not a number, so it could be either positive or negative

Answer 8

the derivative of cosine is - sine

Answer 9

but you are not taking the derivative of cosin(x) you are taking the derivative of cos (1/4 -x)

Answer 10

so you have to use the chain rule and make sure to multply by the derivative of 1/4-x which is -1

Answer 11

therefore you should get
\[\ln(2)\sin(\frac{1}{4}-x)\] there is no minus sign becaues the derivative of
\[\frac{1}{4}-x\] is -1

Answer 12

ok..so heres how i see it.

derivative of ln(2) cos( 1/4 -x ) = 0*cos( 1/4 -x) + ln(2) -sin ( 1/4 -x) .. right?

Answer 13

ohhhh...... i forgot to multiply it by a (-1) for the derivative of the inside..right?

Answer 14

yes you neede that one
you do not need the product rule though

Answer 15

\[\ln(2)\] is a constant

Answer 16

ohhh.... i get it. thanks dude

Answer 17

the derivative of cosine is - sine and the derivative of 4cosine is -4 sine
don't use the product rule for constant multiples, it is a waste of time

Answer 18

yw