For f(x) = 2sinx + (sinx)^3 + tanx find f'(pi/3). Ok, so what I tried was...

Question

f'(x) = 2cosx + cosx(3(sinx)^2) + (sinx/cosx)

pi/3 = (1/2, sqrt(3)/2)

therefore, 2(1/2) + 1/2(3(sqrt(3)/2)(sqrt(3)/2) + (sqrt(3)/2 (2/1))

1 + .5(3 (3/4)) + sqrt(3)

1 + .5(9/4) + sqrt(3)

= 4.982...

but the answer in my text is 6.125. Where did I go wrong?

Answer 1

tanx = sinx/cosx, but

(tanx)' = sec^2(x)

1 + .5(9/4) + 4 = 6.125