Let g(x) = xe 4x (a) Evaluate the following derivatives of g(x). () g'(x) = (ii) g" (x) = (iii) g(3)(x) = (b) Find a formula for the nth derivative of f (x). g(n) (x) = 4x + e-42 4x

Calculate the derivatives (f(g(x)))' and (g(f(x)))' if f(x) = x? 1 g(x) = 5x + 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.) (S(g(x)))' (g(f(x)))' =

find the derivative h(x) = 2 x2 − 8 x8 + 6 x

Find the derivative of each function using derivative formulas. (b) B(x) = e2x + e² (a) A(x) = sec(x) (c) C(x) = 5x³ + 2x (e) E(x)=√x (g) G(x) = ²/ (i) 1(x) = // 2x x-1 (1) F(x) = √√x (h) H(x) = x - 7 (j) J(x) = xe* (d) D(x) =

Find h(x) if h'(x) h(x) = = 9x (3-x²)² and h(1) -3. ==

If g is a differentiable function, find an expression for the derivative of each of the following functions. (a) y xg(x) O xg'(x) xg'(x) + g(x) O xg(x)- g'(x) g(x) – xg'(x) [g(x)]? xg'(x) – g(x) x2 xg(x) + g'(x) (b) y = g(x) O xg'(x) xg'(x) + g(x) xg(x) – g'(x) g(x) – xg'(x) [g(x)]? xg'(x) – g(x) x2 xg(x) + g'(x) (c) y = g(x) xg'(x) xg'(x) + g(x) xg(x) – g'(x) g(x) - xg'(x) [g(x)]? x2 (x)6 – (x),6x xg(x) + g'(x) x2

if f(x) =    2x+1 and g(x) = x3+1 then the derivative of f(g(x)) is?

Calculate the derivatives (f(g(x)))' and (g(f(x))' if f(x) = x³ 1 g(x) : бх + 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.) (F(g(x))' = (g(f(x)))' =

Given f(x)=(2)/(x-1) find f′(4) using the definition of a derivative.

y = (x² + 1 ) ( x + 5 +) Find the first derivatives of