5. What is the definition of the derivative of a function f(x) ?

Q: Sketch the graphs of two functions that have the given derivative: f'(x)=2

A:

Q: 2. how does the knowledge of differentiability and continuity determine the derivative of functions?

A: A function is said to be differentiable if the derivative of a function exists at all points. The…

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: Find the derivative. g(x) = tanh-1(x?)

A:

Q: Find the derivative of the algebraic function.

A:

Q: 9) If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Since you have asked multiple question in a single request, we would be answering only the first…

Q: What is the derivative of h(x) = g(x) - f (x)?

A: What is the derivative of h(x) = g(x) - f (x)?

Q: Your job is to estimate this special base. In other words, estimate the value of b for which, at…

A:

Q: What can we use to find the derivative of a function when it is impossible or difficult to isolate y…

A:

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Here is the graph of the second derivative of a function g(x). g"(x) Where does g(x) have a point of…

A: Inflection point is at that x value where the double derivative of the function is 0.

Q: Find the derivative of the function f(x) = coth−1(x2)

A:

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

A:

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

A:

Q: 3. Sketch the graph of the derivative of the function below.

A: A rough graph can be plotted as values are not given in the given graph.

Q: 1 . Use the definition of the derivative to compute f'(x) if f(x)

A: We use the limit definition of f'(x)

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: Match the graph of the above function with the graph of its derivative. 0 ㅇ O 수 +

A: The given graph of the function is the graph of a semi circle. Or positive side of the circle.

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: -4 Determine the derivative of y =x

A:

Q: g(u) u +1

A:

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

A:

Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

A:

Q: Find the derivative of the algebraic function.

A:

Q: 1, Find the first and the second derivative of f(x): f(x)=x

A:

Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

A:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

A:

Q: What is the derivative of f(x)?

A:

Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

A:

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: Suppose the derivative of f is f '(x)=- At what values of x does the f does have a x slope of -4.

A:

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: 1 Use the definition of derivative to find the derivative of the function f()

A: Solution:

Q: If fox) is odd function , then the derivative of y =coshf(-x)) equals

A: here option B is true

Q: 4. f(x)=

A: The given function is: fx=5x2x+3   As we know that; The Power Law: ddxxn=nxn-1 The Quotient rule:…

Q: 7. Determine the derivative of the function with respect to x. ソミx

A:

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: 10 The derivative of f(x)= - is

A:

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: 10 Use the power rule to find the derivative of f(x) = Vx.

A: Given,          The function is fx=x10 .

Q: 13 Use the power rule to find the derivative of f(x) = 'Vx.

A:

Q: 7. If h(x)=|2x- 3, what is the value of the derivative at x = -2?

A: According to the problem we have

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Find the derivative of f(x) = cot^−1(x^2 + 3)

A:

Q: Find the derivative of the function. 10 f(x) = 3 + 4cos x %3D

A: Given that fx=10x3+4cosxTo find its derivative

Q: 7 Use the power rule to find the derivative of f(x) = x f'(x) =

A: Power Rule: The power for the derivative of the function xa is given by, The given function is f(x)…

Q: 3. Find the derivative of g(x)=

A: We will use Lebnitz rule to find the derivative Of g(x).