Question

Suppose that f '(x)=2xf(x) and f(2)=5. How do you find g '(pi/3) if g(x)=f(secx)

Answer 1

do u know chain rule, (i guess you know)
g(x) = f(sec x)
g'(x) =...?

Answer 2

I thought chain rule was with something raised to a power?

Answer 3

chain rule can be applied to anything of the form \(f(g(x))\)
a function within a function, a composite function
here f(sec x) is composite function of f(x) and sec x

Answer 4

So do I take the derivative of sec x? If f '(x)=2xf(x), 2x is the derivative of x^2 but does that help with this problem?
I know I'm probably over thinking this and making it harder than it is.

Answer 5

g(x) = f(sec x)
differentiating this w.r.t. x
\(g'(x)= [f(sec x)]' = f'(\sec x) \dfrac{d}{dx}\sec x\)
got this chain rule part ?

Answer 6

Yes

Answer 7

and whats derivative of sec x ?

Answer 8

sec x tan x

Answer 9

now to get g'(pi/3), just plug in x = pi/3 !
what u get ?

Answer 10

Let me go back a step for a second,

Is this right?