Write sinh(7 In(x)) as a rational function of x.

Q: S x²-x+1 x² + 2x + 2 2 -dx

A: We need to evaluate integral.

Q: Use the product rule to find the derivative of (6a° – 4xº) (9e" – 5) - Use e^x for e". You do not…

A:

Q: Given g(x) = ln[(x^1/3 + sinx - 3tanx)/3x^4 - x^1/2], calculate g'(x)

A: Given equation is , gx=lnx13+sinx-3tanx3x4-x12 Let's find g'(x) Formulae we are using here,…

Q: Given the function f ( x ), use the formula f ' ( x ) = lim h -> 0     f ( x + h ) - f ( x ) / h…

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Q: Given g(x) =In(10a"+x), the derivative d(x) is %3D

A:

Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: Use the u-substitution to find the anti-derivative of m'(x)= 1/xln(x)

A: solution :- antiderivative is the integration  So put ln(x)  = u Then (1/x )dx  = du And then…

Q: Given the function​ f, find the slope of the line tangent to the graph of f-1 at the specified point…

A: Obtain the inverse of the given function as follows:

Q: Find the tangent line of the function f(x) =16/x− 4√x at x = 4, and the point at which the tangent…

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Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

A:

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: If f(x) = 4x sin-), find f'() = f' (0.4) -

A:

Q: is y=s/(1+s)  a rational function? If not, what type of function is it?

A: Given function,  y = s/(1 + s)  To find whether it is a rational function or not.

Q: sec2 ede tan3 0 + 4 tan 0

A:

Q: sinh 3x –1 H(x)=: 1+cosh 3x –1

A: Given: H(x)=sinh3x-11+cosh3x-1 To solve: The given function.

Q: Find y' by direct differentiation (with respect to x).  y=x7-11x+π3

A: Given:y=x7-11x+π3

Q: function f(x)=2x^3-5x^2+3x+2, find the equation of the tangent line at x=1.

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Q: Q. / Find the derivative of y = (In(x²))'n(x²).

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Q: Find the anti-derivative of the function and evaluate. g(x)=2x g(0)=7

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Q: Write sinh(3 ln(x)) as a rational function of x.

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Q: Use reduction formula to find (tanh" xdx 10

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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: What is the domain of ln |x| ?

A: Given: fx=lnx To determine: Domain of a given function.

Q: Find the difference quotient of f(x) = x² at x = a and simplify. (The difference quotient at x = a…

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Q: use the definiton of a derivative to find the deriviative of f(x)=3x^2+x

A: we have to determine the derivative of f(x) using definition  of derivative .f(x) is given as below

Q: Given g(x) = In(10x° + x), the derivative g (x) is %3D

A:

Q: For the function f(x) = 3x ln x, find f'(x) =

A: Given functionfx=3x4 .ln x

Q: Use the definition of the derivative to determine dx (ax² + bx + c), where a, b, and c are…

A: NOTE: Refresh your page if you can't see any equations. . the definition of derivative is  here we…

Q: d Use the Product Rule to find the derivative [(x + 3)(3x + 8)]. dx Answer

A: Explanation of the answer is as follows

Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

A:

Q: Evaluate the function (a) sinh 3 (b) tanh(−2).     If the value is not a rational number, round your…

A: a). sinh3=e3-e-32     ∵sinhx=ex-e-x2=10.0178≈10.018

Q: Given f(x)=ln(5x), what is f'(x) when x=14.2?

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Q: In the function:  f(x)= (3x^2)ln(x) , x>0 Where is the function increasing and decreasing in…

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Q: Differentiate the function. f(x) = sin(x) In(3x) f '(x)

A: Here, you can use the product rule for derivative. ddx(u·v)=u·v'+v·u'

Q: Write sinh(7 ln(x)) as a rational function of x.

A: Given sin h (7 ln x)

Q: Evaluate the function (a) cosh 0 (b) sech 1. If the value is not a rational number, round your…

A: Solution:- Evaluate the hyperbolic function  a) cosh 0  b) sech 1

Q: Calculate L6 for f(x) = x² + 7|x| over [–3,4]. (Use decimal notation. Give your answer to three…

A: Given f(x)=x2+7x over [-3,4]

Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

A:

Q: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

Q: ind the derivative of h(x) = %3D 4x2+2

A:

Q: Hi, I need help with this step-by-step please.

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Q: For the function f(x) = 10x² – 3x + 5, find the equation of the tangent line at x = 8.

A: We have to find the equation of the tangent line of  f(x)=10x2-3x+5 at x=8.

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: The instantaneous slope of f(x) when f(x) is rational

A:

Q: What are the zeros of f(x) =8 sin x-4 on the interval [0,2r]?

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

Q: Differentiate the following functions: 4. y = In (sec 2x + tan 2x)

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.