Question

Find the derivative f(θ)= secθ^2
How to solve this?

Answer 1

use the chain rule

Answer 2

d/dx f(g(x))=f'(g(x))g'(x)

Answer 3

f(θ) = y
f'(θ) = dy/dθ
u = sec(θ)
du/dθ = sec(θ)tan(θ)
y = u²
dy/du = 2u

Then,

f'(θ) = 2usec(θ)tan(θ)
==> 2(sec²(θ))sec(θ)tan(θ)
==> 2sec³(θ)tan(θ)

I hope this helps!

Answer 4

f(x)=x^2
g(th)=sec th