12. Given the functions f(x) = cos(x) and g(x) 3 = determine the range of the combined function y = f(x) = 2 g(x)
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- 2. Find the derivative of each function: cos (x) 1-x² (b) g(x) = 5³√x - (a) f(x): (c) f(x) = (3x² + x − 12)(7x² − 4x) - (d) s(t) = 2t³ - 8t+43. Find the derivative y(15)of the function y = (x2 + x)sin(2x).A2) Find the derivative of the following functions: r2 + 5 q² – 5 (a). f(x) (b). f(x) = 2 tan (x) – 5º (c). f(x) = (x + 5 sin æ) (1 – 4 cos ) tanx (d). g(x) = secz
- The graphs of the functions f and g are shown below. y y 8 7 g(x) 6 f(x) 2 5 4 NA AZ 3 1 2 1 -1 1 2 3 1 2 3 -1 -3 -2 -1 (b) For p(x) = g(g(x)), determine p'(4) = Use the graphs above to determine the following quantities. If a quantity is undefined, enter "DNE". (a) For h(x) = g(f(x)), determine h'(0) = 4 (c) For w(x) = f(g(x)), determine w' (1.5) 5 = -3 4 5 XC) Find the derivative of y= (1 + x²)*3. Consider the function f(x) = e¯ 4x2 – 2 (a) Show that the second derivative is f"(x) (b) Find all intervals where the function f(x) is concave up or concave down.
- Fnd the derivative of the following functions. 6. f(x) = (2x³ - 3)(x² – 4x) 5x-3 7. h(x) = %3D 8. g(x) = x2 cscx %3D 9. z = e*V - 2e* cosx tan x 10. dx (cos.x-4Please answer letter BA2. Find the third order derivative of the following functions: a. F(x) = 3x³ - 5x+12 Y=3t+ 2et b. C. Find the Inverse Function (f¹), where f(x) = 2x+6