To develop antiderivative rules, we need to think about derivative rules backwards. In Calculus 1, you learned the power rule for taking derivatives. Which of the following is the power rule for finding antiderivatives? The antiderivative of æ" is n+1 1 - xn+1 + C The antiderivative of æ" is a"-1 +C

Q: On which derivative rule is the Substitution Rule based? Choose the correct answer below. O A. The…

A: Substitution rule:

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x =1, assuming…

A: Given, f(1)=4, f'(1)=-1 y=4xf(x) y'=(4xf(x))' =>y'=4(xf(x))'

Q: 1. Consider the function f(x) = x³ – 3x?. a. Sign analyze f (x). b. Find the derivative, f'(x). C.…

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Q: 7. Use the definition of the derivative (long method/ increment method) to find the derivative of…

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Q: If f(1) = 3, f'(1) = 4, g(2) = 2, and g'(2) = 8, find F'(1). F'(1) = ... NOTE: This problem is a bit…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: derivative

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Q: We need to think backward here: What function do we know has a derivativeequal to the given…

A: Given that the derivative is F(x) = x2   So, we have to find the antiderivative of F(x)

Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. ƒ(x)…

A: We find the antiderivative of f(x). C=integrating constant

Q: 18. Find the derivative of the function using shortcut rules. Simplify for extra credit. 7 f(x) = x4

A: Explanation and solutions is given below.....

Q: 4x - 4 if x > 2 Suppose f(x) = Find f'(2) using the definition of derivatives. if x < 2

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Q: find the derivative 1).f(x)=X^3(X^4/3-1)…

A: 1)

Q: OLVE THE FOLLOWING: What is the derivative of.6x* – 7x3 + 5x² ? What is f'(x) if (x) = (2x² + 1)(x²…

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Q: Suppose that the function v in the Derivative Product Rule has a constant value c. What does the…

A: We Will find the solution to the derivative problem.

Q: 8. Find the derivative of the following functions with respect to x by using either the product or…

A: Part (a):   Apply the product rule:

Q: Domain: (-infinity,1) U (1,3) U (3, infinity) f'(x)>0 for (x 3). f''(x)>0 for (-2 3). f''(x)<0…

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Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: From the left side of x=1, the derivative is

Q: Use the quotient rule to find the derivative of 8e" + 4 - 9x7 + 9x° Use e^x for e". You do not need…

A: We will find the derivative.

Q: In another universe, there are some extra functions that their mathematicians use: stars, sun and…

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Q: pts) Use the following table to find f(g(x))· g(x) for x = 1. Hìnt: start by writing out the dx…

A: Concept : product rule for derivative is d(f(x).g(x))dx = f'(x) g(x)+g'(x)f(x)  given ddx…

Q: Find the global extrema of f(x) = xln(x+2) on the interval [-1,2]. You should demonstrate how you…

A: We have to find the value of x for extreme point.

Q: x + Va x2 1. Find the derivative of the function f(x) = in two different ways. Once with the…

A: 1 Given function,                  f(x) = x+xx2Differentiate f(x) with respect to x, using quotient…

Q: On what interval is the function f(x)=x^2e^x concave downward?

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Q: Jsing only exponential (e*), cubic (x³), and the cosine (cos x) functions, create anot unction for…

A: To find: A function using the given functions for which the derivative computation requires using…

Q: In this question, we use derivative rules to compute the derivative of f(æ) = 1/2 7/6 a) First…

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Q: 27 1, 2. -1 1 2

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Q: belov are four types of functions. VWnich does not possess a derivative of the same type? a)…

A: To find which function does not possess a derivative of the same type?

Q: Q4: 1+x h (x) so (2x² + 1)² (2x² + 1)² (1) – (1 +x) 2 (2x² + 1) (4x) h' (x) = (2x² + 1) [(2x² + 1) –…

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Q: If f(x)= x2 +4 then what is the derivative off at x=-1? %3D Solo

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Q: On which derivative rule is the Substitution Rule based? Choose the correct answer below. O A. The…

A: Substitution rule:

Q: Write down the solution and Choose the correct answer Q1) The dervative of the function f(x)=x+2…

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Q: Find the derivative of g(x) using first principles. Show your steps. f (x) = %3D 1+3

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Q: 3.2 2. 3t (t 8-4れt。75 ニ

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Q: The following is a step in the evaluation of the derivative of a function f(x) at a point x = 1…

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Q: se Richardson extrapolation method to determine the first derivative of f(x) at x = 0.23 for the…

A: Richardson extrapolation f'x=fx+h-fx-h2h Here values at x of function is given and h=.02

Q: Use limits to compute the derivative. f'(0), where f(x) = x ° + 3x +2 %3D f'(0) = (Simplify your…

A: The limit definition of a derivative, is given by f'(x)=limh→0f(x+h)-f(x)h

Q: The graphs of S and g are shown below. (a) derivative does not exist, explain how you know. Evaluate…

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Q: We need to think backward here: What function do we know has a derivativeequal to the given…

A: Given function,H(x)=lnx +e2xwe have to find a function has a derivative equal to the given function.

Q: y=x(tan^-1)(2x)-(1/4)ln(1+4x^2) find derivative of the function: full steps please

A: The given function is

Q: A student wanted to take the derivative of e“, using the chain rule. They thought that: • the inner…

A: We have to find the derivative of the function and spot the error the student made.

Q: The 2nd derivative of a function at point P is 0, and concavity is positive for values to the right…

A: Concavity is positive or negative?

Q: I. Use the definition of the derivative f'(x) = lim 7&+h)=Jx) to find the derivative of the…

A: Formula: limx→axn -anx - a = nan-1 Given: R(z) = 6z3+18z5-13z10

Q: Two hours after taking the medicine, the patient's temperature is decreasin Find T"(2). T"(2) =…

A: Given, fx=5x+245x-25

Q: Suppose k is a real number. Use the definition of the derivative to find f' (x), where f(a) = k/T.…

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Q: Use double derivative method for the function y=x- 12x + 48 x²– 64 x to find i) the extreme values.…

A: If a function is f(x), then we need to find the critical value by using f'(x)=0. Extreme values: If…

Q: Find the value of deriVative beloW 3 If x*y5 + x?y³ – xy² + 5y + (x²y+)² = x), then 3y'at(-1,2) = O…

A: derivarive of functions in product and using chain rule of differentition

Q: f(x) = 2 Lim f(x+x) - fox) AX f'(x)= 4x40 Lim AXO Lim (x+4x)² - + (x+AX)^2-x²² AX AX x= x + 2x (0x)"…

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Q: 5 Find the derivative of f(x) = -4√x + T8 Type your answer without fractional or negative exponents.…

A: To find the derivative of the given function.

Q: I. Solve for the derivative of the functions using chain rule. Box your final answer. 3 1. f(x) =…

A: Since you have posted multiple questions i can do first three question as per our company guidelines…