Question

Differentiate.

f(x)=(cos x)/x

I got to here:

(-x sin x - cos x)/x^2

Find the equation of the tangent line to
f(x)=sec x - 2 cos x at (pi/3, 1).

Is the slope 3 times sqrt of 3?

Equation is y=3 times sqrt of 3x - pi times sqrt of 3 +1??

Answer 1

(f'(π/3) = (-π/3 * √3/2 - 1/2)/(π/3)^2
= -(9π-3√3)/(2π^2)

If we call that slope m, then the tangent line is

y-1 = m(x-π/3)