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

Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

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

A: we know that     sinhx = ex-e-x2 Also we know that     n ln(x)=ln(xn)

Q: 1-x e) f(x) = 1+x

A:

Q: Find the derivative of g(x) = In(sin²(ed/x)).

A:

Q: Use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Take the derivative of the following function: f(x)=- + 6/x Express your answer as a single fraction…

A:

Q: Find the derivative of the function 2- X= x"sin? (x³)

A: We know that, from the product rule of differentiation ddxfx·gx=fx·g'x+gx·f'x             ⋯⋯1 Now,…

Q: Use the first principles to find the derivative of cos(x -4x).

A: By the first principle  f'(x)=limh→0f(x+h)-f(x)h. So, dcosx2-4xdx=limh→0cosx+h2-4x+h-cosx2-4xh…

Q: Differentiate and find the second derivative. g(x)= ex(x3+2x) What is g''(x)=

A:

Q: Find the derivative of the function.. 8 7 h(x) 218 4 х - h'(x)=

A: To find the drivative of the given function y=h(x)

Q: If f(x)=3sin(x)+4x^x, find f'(2). Using logarithmic differentiation.

A:

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: Find f′(x). f(x)=5x4 ln x

A:

Q: Determine whether the following statement is true or false, and explain why. The derivative of ln kx…

A: if y = ln x Then y'=1x

Q: Find the second derivative. f(x) = 5e−x − 3e−5x f ''(x) =

A: Recall the following facts.

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 the 3rd derivative, f(3)(x), for f(x) = 6x3/2+e-3x-sinx and simplify with positive exponents.

A:

Q: Find the derivative. y = In {(x + 1)(2x + 9))

A: Derivative of any function is the rate of change. It represents the amount by which the function is…

Q: If f(x) = 2x + ln x, find f-1(2).

A: The function is given as fx=2x+ln x......(1) The value of f(x)=2.......(2) Equate the equation (1)…

Q: use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the slope of the graph of the function at the given point. F(x) = 4x5 + 5x - sin(x), (0, 0)…

A:

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

A:

Q: What is the domain of ln |x| ?

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

Q: Find y" by implicit differentiation.   x4 + y4 =a4

A: Given function is Differentiating both sides  with respect to x, we get

Q: For f(x)= e^x (sinx), find the second derivative.

A:

Q: f(x) e3x+1 lnx³

A: Here we have two functions in the right hand side. That is f(x) is the product of two functions. So…

Q: Use the product rule to find the derivative. Simplify the result. P [(3x + 7)(x² + 2x)] dx

A: See the details solution in below

Q: Find The First Derivative  y = (x2 +5x)3

A:

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

A:

Q: Find the second derivative of h(x)=x2+3x-3 Simplify your answer, if possible.

A: Our objective is to find the second derivative of h(x)=x2+3x-3.

Q: Find the second derivative of the function. 9. g(x) = x-1 10. h(x) = sinx = (x)6

A:

Q: Find the derivative of g(x) = ln(2x + 5)

A:

Q: g(x) =e*(2x² – 3x)

A: g(x)=e^x (2x^2-3x)

Q: Find the second derivative of the function. In(x) f(x) = + 6x? -4x° – 18xln(x) + 3-6 ln(x) + 12…

A:

Q: Find dx by logarithnic differentiation. (3x-2)(x"+3)

A: d(logx)/dx = 1/x

Q: what is -sinh(x) equal when x = 0

A: We know that   sinh(x)=ex-e-x2 Then -sinh(x)=-ex-e-x2 now substituting x=0 in the above equation…

Q: Find the derivative of the irrational function y=2√x−33√x.

A: Given: y=2x-33x

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

A:

Q: Find the derivative of the function. 9x + 1 h(x) = In 4х - 2. h'(x) =

A: Solution: The objective is to find the derivative of the given function

Q: 6x = 4

A: Simple differentiation problem...

Q: Find the indefinite integral of the following function:

A:

Q: What are the domain and range of f (x) = ln x?

A: Given function:   Domain: The domain of a function is the set of  input  values for which the…

Q: Does the graph of y = sqrt(x) - ln x, x> 0, have an inflection point? Try to answer the question…

A: To determine if the function has an inflection point.Part (a) By GraphingPart (b) By Calculus

Q: Find the derivative.

A:

Q: 6x 2) = 4 y7

A: 2) Given- 6xy7=4 To find- The derivative of the above expression using implict differentiation.

Q: (4) Find the derivative of h(x) = 5x³esec(x) .3 %D

A: We need to find the derivative of

Q: X = t-1 2-1

A: Given that x=tt-1,y=t2t2-1. Compute the first derivative.…

Q: What is the derivative of : ln cos 3x

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.