1-t For which functions does y' ? Select all that apply.

Q: y = In(x + Jx² +1)

A: This question is based on differentiation.

Q: Solve the second derivative forf(x,y, 2) = e

A: Given f(x,y,z)=esin(x²+y²)/z To find del²f/delx²

Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: find (y') by Implicit differentiation e(2x+3y) = x² – In(xy³) 1 Add file

A:

Q: Q1:- Find the first order derivative of each of the following functions: e) y = 1 + x'nx

A: Given that y = 1 + xlnx . We find its first derivative. We know that d(xn )  /dx = nxn-1  Here i…

Q: compute the derivative. c(t) = 1-li – e2'k - e2

A: Given  ct=1ti^-e2tk^

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: Find y" by implicit differentiation. x2 + 9y2 = 9 y" =

A: Here we have to find the both y' and y"

Q: use the Chain Rule to find the derivative. y = cos3(e4θ )

A: Given: The function given is  y=cos3(e4θ)   To determine: The derivative of the function y=cos3(e4θ)…

Q: use the Chain Rule to find the derivative. y = cos3(12θ)

A: Here given as y=cos312θ

Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y

A: Given that a function f(x,y) is continuously differentiable on an open region, we can derive the…

Q: Find y' by implicit differentiation. 1) x²y° = 2

A: Given equation: x2y9=2 To find: y' by implicit differentiation.

Q: Find the first derivative of the function g(x) = V5 +x +4cos (2x).

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find a formula for the nth derivative y^n of the function y=(x+5)^1/2

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Q: Find derivatives of the function defined as follows. y = e-8x

A: We have to find derivatives of the function: y=e-8x We know the formula of derivatives,…

Q: Use the Chain Rule to find the derivative. y = cos3(e4θ )

A: We have given y=cos3e4θ Then, dydθ=dcos3e4θdθ=3cos2e4θ-sine4θ4e4θ=-12e4θsine4θcos2e4θ

Q: B) Find for the Implicit function: dx x2 - sin(xy) + y² = 5xy

A:

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

A:

Q: Q2: - Find the second derivative of the following function at x = 2 15 marks 1) y=+ V 2) y 3 (x +)…

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Q: 3. Find the *_ 2° L_weak derivative her XE [0,2TC] XE

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Q: Use the Chain Rule to find the derivative. y = cos3(12θ)

A: Given function is y=cos312θ. To find the derivative of the given function using chain rule.…

Q: 2. g'(x) where g(x)=x² +7x-5 %3D

A: In this question we need to find a derivative of the given function.

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

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Q: f. y=In(x8+1)

A: We will solve the problem

Q: Find y" by implicit differentiation x2 5y2 5 + = 2 X у"-

A: Take d/dx on both sides and distribute it on the left side. Derivative of constant =0

Q: Find the derivatives of the function defined as follows.

A:

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

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

Q: by implicit differentiation if x² +9x+9xy-y² =16 Find x dy

A: Find dydx by implicit differentiation if x2+9x+9xy-y2=16. Solution: Power rule of differentiation…

Q: Find y" by implicit differentiation.   x3 + y3 =1

A: We find y' first

Q: 5х f(x) = 2) Find the first derivative given that J2x+3

A: Solved below...

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: Find the derivatives of the functions k(x) = x2 sec (1/x)

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Q: Find the differential of the function y=xex2.

A: Here the given function as Use the product rule of derivative which states

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given, f(x)=sin(2x)+17

Q: Find y" by implicit differentiation. x² + 9y2 と y"

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Q: 1)™ Determine a formula for the derivative of (x° + that works for any integer m. m y'

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Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

A:

Q: Q2: - Find the second derivative of the following function at x = 2 1) y=+ V

A: ddx1x = -1x2 ddxxn = nxn-1 ddxx =12x

Q: 6. v(y) = In (y² – 8y – 1)

A:

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: Find the first derivative of the following implicit function: X² + 3xy + y² = 4

A: Given : x2+3xy+y2=4 Lets take first derivative  Take derivative with respect to x. apply the power…

Q: Find the first derivative of the following implicit function. x² + 3xy + y² = 4

A: Given : x2+3xy+y2 = 4

Q: f(x) = e²x cos(x) e2

A:

Q: Find for the Implicit function: dx x² – sin(xy) + y² = 5xy

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Q: Q1) Compute the derivative of the function f (t)= | sin² x²dx. -t

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Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): x²(x + 1),…

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Q: Find the derivatives of following functions e2x f(x) 1- ex

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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.