6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the following gives a correct expression for h'(x)? (A) 20(g(x))³ = 20 (e²x + x)³ x-Sy 20(g(x))³ = 20 (2e²x + 1)³. (B) (C) (D) 5(g(x)) = 5(2e²x + 1)² 20(g(x))³ g(x) = 20 (e² + x)³ (2e²ª + 1) +5x4 e2(5.4) 4 10x² +5+

Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x + h) = Simplify the difference quotient, f(x+h)-f(x) h f(x+h)-f(x) h The derivative of the function at a is the limit of the difference quotient as h approaches zero. f'(x) = lim f(x+h)-f(x) h→0 h

Letf, g be functions. Suppose we know that ƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3. Using the above information, compute h' (-6) where h(x) = (f(x))² g(x). h'(- 6) = Number

Suppose that for the functions f(x) and g(x), f'(x) = g'(x) on [10, 12] ƒ(10) = 9 g(10) = -9 ƒ(12) = 11 What is the value of g(12)? Provide your answer below: g(12)=