What is the difference of antidifferentiation and anti-derivative?

Q: What is the First Derivative Test for Local Extreme Values?

A: What is the First Derivative Test for Local Extreme Values?

Q: What is the shape of a graph in application of derivatives?

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the fourth derivative of ƒ (z) = 2z¬3 f(4) (z) –

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Q: Find the second order derivative if  y = xx

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Q: What are the the mean value theorem in application of derivatives?

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Q: 2=D5 +y

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Q: What is the meaning of a derivative?

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Q: 6. R(z) Vz3 8z4

A: ddxxn =nxn-1ddx1xn =-nxn+1 ddxx =-12x

Q: Why is the derivative of a constant function zero?

A: Consider the constant function fx=k. Apply the derivative definition as follows.

Q: -a ; Y 5.)(*+y)² +(x-y)

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Q: On which derivative rule is the Substitution Rule based?

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Q: Explain how to apply the Second Derivative Test.

A: The second derivative test is used to find the relative maxima or relative minima. The second…

Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: We have to tell If the sign of the first derivative function is positive , the main function f(x) is…

Q: Find the derivative of f(x) = x + 4". f'(x) = %3D

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Q: Explain why the derivative of a constant function is 0.

A: We have to explain that derivative of a constant function is 0. We know that constant function is…

Q: How do you find the derivative of a constant multiplied by afunction?

A: If f(x) is any function and let y=cf(x)            function f(x) multiplyed with a constant, c is…

Q: What is the derivative of * 3lnr?

A: Given that y=3ln x find the derivative

Q: Are critical numbers from the first derivative used in the test for concavity?

A: We have to tell that  critical numbers from the first derivative used in the test for concavity or…

Q: What is the derivative of f(x) equals the third square root of x times the fifth square root of x?

A: Given function is

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Describe the Second Derivative Test in your own words

A: A second derivative test is conducted to find the relative maxima and  minima of a given function.

Q: . Find the second derivative of y = 5sin x – 3ln x.

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Q: Determine the anti derivative of the function.

A: Given Data: Function: fx=2x35+10x5-74x Similified the given function f(x).…

Q: Find the derivative. y = (lnx) 2

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Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: What are the applications of these derivatives?

A: First derivative tells the rate at which the original function changes.  Second derivative tells the…

Q: How can the derivative function definition be applied to this problem?

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Q: Find the derivative of the function. Vs - 4 f(s) = Vs +2 f'(s) =

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Q: Find the derivative of y = x. %3D

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Q: Find the first and second derivative if w = 3z-2-(1/z)

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Q: What is a higher-order derivative?

A: We create, or derive, a new function f'(x) from a function f(x) called as derivative of function…

Q: one leg of a right triangle is 1 in/min and the other leg increases 2 inches per min. What is the…

A: Let the first leg of the right triangle be a and the other leg be b. Let the hypotenuse of the right…

Q: the derivative of

A: We find derivative of given function Use formula sin2x = 2sinx cosx

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

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Q: Explain how the Second Derivative Test is used.

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: Find the portial derivative of

A: Follow 2nd step.

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: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: What is the derivative of y = 3lnx) Y :

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Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: Find the derivative of fx Fx=8x3 cot x

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Q: What is the derivative of cy = 2 - a°y ?

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Q: State the second-derivative test for functions of two variables.

A: State the second - derivative test for functions of two variable.

Q: Compute for the derivative of 3 y = х |

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Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule & formula.

Q: Find the derivative of f(x) : %3D

A: We need to differentiate the function f(x)=1x with respect to x. We also know that ddxxn=nxn-1.

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

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Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…