For the derivative of f(x) = 4e2r3 Identify the inner and outer functions of the composition,...
LI Write the composite function in the form f(g(x)). [Identify the inner function v = g(x) and the outer function y = f(u).] = V1 + 8x (g(x), f(u)) = Find the derivative dy/dx. dx X
5. Find the derivative matrices of the following composition of functions. (а) fog where f (x, у) — 2х — 3у, g(u, v) - (usin u, U sin u) (Ъ) f.g where f(х, у, 2) %3D (x? + у? +2?,х— у+2:), g() %3 (2, 13, 2/4) (с) fog wherе f (x, у, z) 3D (хуz, ху + xz — yz) where g(u, v, w) %3D (uu, uw, vw)
5. Find the derivative matrices of the following composition of functions. (а)...
Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] (96%), f(u) = ( 0,- 1 x)
eca Problem 3. Write down f(x) = as a composition f = goh of an expo- nential function g and a power function h. Then apply chain rule to compute derivative of f. (3+4 points) Bonus Points: For the functions g, h found in Problem 3 above, write down the composition h o g, composition of them in the other order. Call this new function F. Argue why F is not the same function as f. Then apply chain rule...
Use the composition of functions to determine if f(x) and g(x) are inverses of one another. 12. f(x) = 7x - 1 ; g(x) = x - 1
FIND THE DERIVATIVE OF THE
GIVEN FUNCTIONS!
2. f(x) Vx+3x-1 3. f(x)=x(x -x)
. Express H(x) = 3 √— 5x2 − 3x as a composition of two functions, f and g, where ( f ∘ g )(x) = H(x).
Find the derivative of the following functions: (x2-1) f(x) = (x2 +1) f(x) = (x3 + 2x)3(4x + 5)2
Find the requested composition of functions. Given f(x) = 7x + 11 and g(x) = 5x - 1, find (f ∘ g)(x).
Find the requested composition of functions. Given f(x) = 4x2 + 3x + 6 and g(x) = 3x - 8, find (g ∘ f)(x).