Question

Given the following functions: 𝑓(𝑥)=(𝑠𝑒𝑐(𝑥)); g(x)=x^4+5

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

Answer 1

d/dx f(g) = df/dg * dg/dx

f(g) = sec(g), so
d/dx f(g) = sec(g) tan(g) * 4x^3 = 4x^3 sec(x^4+5) tan(x^4+5)

d/dx g(f) = 4sec^3(x) * secx tanx = 4sec^4x tanx