"Find f '(x) and f '(c)." for function "f(x) = (sin(x))/x", c = pi/6

[Frenchi33]

"Find f '(x) and f '(c)." for function "f(x) = (sin(x))/x", c = pi/6

Directions: "Find f '(x) and f '(c)."

Function: "f(x) = (sin(x))/x"

Value of C: "c = pi/6"

I found f '(x) which is "(xcos(x)-sin(x))/x^2", but what is f '(c)? I just assume you'd plug in "pi/6" for x in the derivative, but it's not the right answer on my digital homework.

Thanks!

 

[Knorrhane]

Directions: "Find f '(x) and f '(c)."

Function: "f(x) = (sin(x))/x"

Value of C: "c = pi/6"

I found f '(x) which is "(xcos(x)-sin(x))/x^2", but what is f '(c)? I just assume you'd plug in "pi/6" for x in the derivative, but it's not the right answer on my digital homework.

Thanks!

f'(x)=cosx/x - sinx/x^2

 

[Deleted member 4993]

Directions: "Find f '(x) and f '(c)."

Function: "f(x) = (sin(x))/x"

Value of C: "c = pi/6"

I found f '(x) which is "(xcos(x)-sin(x))/x^2", but what is f '(c)? I just assume you'd plug in "pi/6" for x in the derivative, but it's not the right answer on my digital homework.

Thanks!

First derivative is correct. May be the answer needs to be further simplified.

 

[JeffM]

Directions: "Find f '(x) and f '(c)."

Function: "f(x) = (sin(x))/x"

Value of C: "c = pi/6"

I found f '(x) which is "(xcos(x)-sin(x))/x^2", but what is f '(c)? I just assume you'd plug in "pi/6" for x in the derivative, but it's not the right answer on my digital homework.

Thanks!

You did not tell us what you got for \(\displaystyle f'(c)\).

Did you use a calculator? Did you set it to radian measure? Perhaps an exact answer is wanted rather than a numerical approximation.