E. If f(x) = sin x + In x, find f'(x). Check that your answer is reasonable by comparing the graphs of f and f'. %3D x)/x

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

A:

Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: The linear approximation at x 0 to sin(2x) is A + Bx

A:

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Use implicit differentiation to find dy given y³2 – log(x²y¹) = cos¯¹(1). dx

A:

Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

A:

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)<0 and f(b)<0.…

Q: Find dy/dx by implicit differentiation.

A:

Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find d dy dx

A:

Q: Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary…

A: let ∫x-necxdx for n a positive integer and c a non zero constant is non elementary since…

Q: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

A:

Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

A:

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: 1. Find the centered difference approximations of 0(h^4 ) for the first derivative of y=sin(x) +…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

A:

Q: Integral of e^(4x)sin(4x) dx

A:

Q: 53. df = (x+ 1)ye"dx + xe*dy

A:

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: The derivative of y=eov? +cosh/x equals Select one: O y' = 2/x et +sinhx + sinh/x O None O y'=@ov +…

A: This is a composite function. Therefore we have to use rules for derivative of composite functions.

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: Let y = In(x'e2x ). Find dy/dx.

A:

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

A:

Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

A:

Q: What is the first derivative of s(r) = log, sin z 712+8z+2 Provide your answer below: s'(x) =]

A:

Q: The most general antiderivative of x sin(3x) is

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

A:

Q: dy Find by implicit differentiation. d x e COs x e2y

A: Given query is to find the dy/dx using implicit differentiation.

Q: The derivative of y =e' ,In(sin 2x) is a) y = eln(sin 2x) sin 2.x b) y = e a(sin 2x), cos 2.r c) y'…

A:

Q: 10. Let y = In(x' + sin 3x). Find dy/dx.

A:

Q: Find the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

A: Solution

Q: sinh x – 1 dx cosh x

A: The given integral,        ∫sinhx-1coshxdx

Q: Find an equation of the tangent line to the graph of {(=) = [. t cosh (t² – 1) dt f(x) /1+ln (x)…

A: First I have written the rule of derivative of an integral to find the slope of tangent line for…

Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

A:

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

A:

Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

A:

Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

A:

Q: Find the relative extrema of f(x) = (x − 1) cosh x − sinh x.

A: Maxima and minima: f(x)=(x-1)coshx-sinhx f'(x)=(x-1)sinhx+coshx-coshx f'(x)=(x-1)sinhx…

Q: B4. Evaluate e* sin x dx by using integration by parts method.

A:

Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

A:

Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

A:

Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.

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.