Suppose f(t) is a continuous function over the interval (0, ∞o), but you know only the following values of f(t): t f(t) 4 6 Use a substitution to evaluate the integral ƒ' (√) dz. 1 2 3 14 Give the exact answer. 5 6 7 8 9 10 11 7 16 18 12 9 5 Please be aware that the function in the integral is f', which is the derivative of f. You may assume that f is differentiable and f' is continuous everywhere.

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: 9. Let f(x) = cos 2x. Calculate f(50) (x), the 50th derivative of f(x).

A:

Q: Consider the function f(x) = 3x² + 30x + 83 Determine an expression for the derivative of f(x).

A: f(x)=3x2+30x+83

Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

A:

Q: (d) Let h(x) g(f(x)). Use the figure below to find h'(1) or state why the derivative does not exist.…

A:

Q: Calculate the derivative of the following function. y=f(g(4x)), where f and g are differentiable for…

A: Using chain rule of differentiation

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: Find the derivative of the function. 14) f(t) = (3 - t)(3 +3)-1 %3D

A: Given the function f(t)=(3−t)(3+t3)−1

Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.

Q: f the function defined by 1 F(x) x2 =. * dt the produat rule ond the FTC II

A: Introduction: The Leibniz rule for differentiation under the sign of integration is given by,…