Write cosh(In(x)) as a rational function of x.

Q: use the Product Rule to calculate the derivative. f (x) = (3x − 5)(2x2 − 3)

A: use the Product Rule to calculate the derivative. f (x) = (3x − 5)(2x2 − 3)

Q: Use the first derivative test to find the location of all local extrema for .3 f(x) = +4x*+7х— 5 3

A: For extreme values we find critical points by putting f'(x)=0

Q: Use the chain rule to find the derivative of f(x)= 4(2x^3−4x^9)^12  f'(x)=_______

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Q: 5. Integrate using Rational Functions: xp: (x+ 1)³`

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Q: find the derivatives of f(x)= (-3+x^-3)(-4x^3+3) using product rules.

A: We need to find the derivatives of f(x)= (-3+x^-3)(-4x^3+3) using product rules.

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

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Q: Differentiate the function In x f(x) = In 2x +3, x>0

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Q: Find the absolute extrema of f(x) = x3 +5x2-8x+2 on the interval [−1, 2].

A: Given function is fx=x3+5x2-8x+2 ; x∈-1, 2

Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

A:

Q: Find q′(x) from q(x)=−5x3+x2−3x−3 using the definition of a derivative. (Do not include "q′(x)=" in…

A: Express the mathematical expression for the definition of derivative. f'(x)=Lth→0f(x+h)-f(x)h Given…

Q: Find q' (x) from q(x) = -5x³ + x2 – 3x – 3 using the definition of a derivative. (Do not include "q'…

A: Given, q(x) = -5x3 + x2 -3x -3  Differentiating q(x) with respect to x  d[q(x)]/dx = q'(x) q'(x) =…

Q: find the extrema of f(x) =2x3-6x on [0,3]

A: Given:

Q: Write cosh(In(x)) as a rational function of x.

A: write coshlnx as a rational function of x

Q: 1. X > VX + 4 3+x 2. > 8 x+1 3. 4X 2 2 X+2

A: Since you have asked multiple questions, we will solve the first three questions for you. If you…

Q: Use the Product Rule to find the derivative of the function.

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Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

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Q: Write cosh(ln(x)) as a rational function of x.

A: Cos h (lnx)We knowCos h (a) = ea+e-qzsoCos h (ln x ) = elnx+ e-lnx2                       = x+1x2…

Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: Find the derivative of the function f(x) = 3x2- 13x 25 by definition of derivatives f(x + h) - f(x)…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Use the chain rule to find the derivative of f(x)=5e^(3x^9−6x^10) f'(x)=____

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Q: find the derivative using the definition g(x) = 2x2 + 1

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Q: Find the absolute extrema of f (x) = 2x – 3x² – 12x +1 on the interval [-3,3].

A: fx=2x3-3x2-12x+1 Differentiating with respect to x, we get f'x=23x2-32x-121+0=6x2-6x-12 Now to find…

Q: What is the length L of the interval on which the function f(x)=x4e−x is increasing?

A: Given

Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: Use the product rule to find the derivative of the function f ( x ) = ( x 2 - 3x + 2 ) ( 4 x 3 - x 2…

A: Given- fx=x2-3x+24x3-x2+4 To find- The derivative of the above function. Concept Used- The product…

Q: Find the derivative. g(x) = (4x – 2)° – Vr + 8

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Q: Use the chain rule to find the derivative of f(x)=3e^−4x^9+3x^3   f'(x)=

A:

Q: Find the intervals of monotonicity of the function f(x)=xlnx.

A: Here the given function is Use the product rule of derivative

Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 - 2x + 5)(x³ - 6) g'(x) =

A:

Q: Calculate the slope, m, of the tangent line to the rational function f at x = 10. %3D f(x) = %3D x -…

A: Given: The tangent line to the rational function f at x=10 We have to calculate the slope.

Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: Use the product rule to find the derivative. f(x) = (3x - 2)(6x + 1) %3D O f(x) = 36x - 4.5 !3! O…

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Q: Suppose that f(x) = 17ex - exe Find f'(3)= ?

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Q: Given f(x) = 5x² + 5x + 2, find f' (x) using the definition of a derivative.

A: Given function is solved through derivative  detailed solution is given below

Q: write cosh(4 ln x) as a rational function of x

A: To solve the given problem apply the following formula

Q: Can you please help me find the derivative of f(x)= (2x-3) / (x3-8x+9)

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Q: Use the f'(x)=limh->0f(x+h)-f(x)/h  to find the derivative of f(x)=11x2 AT x=1

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Q: find the derivative of g(x) = (x+5)/(5-2X) using the definition of the derivative. must show all…

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Q: The graph of a polynomial function, f(x), is shown above. In the interval shown, how many times with…

A: We know that for any functionfx, the second derivative of fx cross the x-axis means second…

Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

A:

Q: Find the intervals of monotonicity of the function f(x) = 4.

A: Intervals of monotonicity means we have to finds intervals in which function is inreasing or…

Q: Find the absolute extrema of f(x) = 2x3+3x2−12x on the interval [0, 2]

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Q: f '(x) by using the definition of the derivative. f(x) = 4 – 6x2

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Q: Find the absolute extrema of f(x)=x^3-6x^2+5 on the interval [-3,5]

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Q: Find the derivative of the function f(x) = 8x² – 14x by the definition of derivatives f(x+h)-f(x)…

A: Given function: fx=8x2-14x

Q: sketch the following rational functions by determining all critical values. f(x)=3x2-x3/x2-9

A: The given function is f(x) = 3x2-x3x2-9,This function is not defined at x = -3, x = 3.We try and…

Q: Find and classify the extreme values of f(x)= 6x* –4x° over the interval [-2,2].

A: Given,  f(x)=6x4-4x6

Q: Make a sign diagram for the derivative of the rational function. 6 f(x) = x + 3 f'(x) < 0 undefined…

A: Given function, fx=6x+3

Q: Find an approximation that is accurate to three decimal places to the zero of f (x) = x³ -3x- 1 in…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.