for all of dx 1- y = xvInx 2- y = 3 x(x-2) x²+1

Q: Find in terms of x and y. dx2 x²y2 – 4x = 3 -2xy4 + 4xy² + 4 dy dx2 x

A:

Q: Xtan+4]dx - xdy= of + y]dx - xdy=0

A: Given differential equation is xtanyx+ydx-xdy=0 This equation can be rewritten as,…

Q: d/dx (dy/dx)` x=1, , where y = x3 + 2x - 11

A: To find: The value of ddxdydx at x=1. Given: The function is y=x3+2x-11. Formula used: Power rule of…

Q: Find for all of : dx 1- y = xvInx x(x-2) x²+1 2- y =

A:

Q: Evaluate dy/dx at (-3,1) for x3+(7+xy)5/2=82/3+y2

A: Given:

Q: Find the first and second derivatives. 3 y = 5x-12x-4x dy dx d²y dx2 %3D

A:

Q: 16- y? V16 - x2 x dx dy 2.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Let ƒ(x) = x3 - 3x2 - 1, x>= 2. Find the value of dƒ -1/dx at the point x = -1 = ƒ(3).

A: We will need inverse function theorem. Statement of the theorem is:

Q: Q4 Find dy for all of : dx 2- y = 3 x(x-2) x2 +1 1- y = xvInx

A:

Q: Find * dy ,If y 3 dx + x O x^2 + x O x^3 + x^2 +1 O x^2 + x + 1 O 3x^2 + 2x + 1

A:

Q: 3. Differentiate y = 2x-1 - with respect to x and then evaluate 2 x(x – 1) -dx (2x – 1)2

A: Given and

Q: find the function y(x) satisfying dx/dy=5x ^(-6/7) and y(-1)=-2

A:

Q: What is the I.F of (2y^2+3x)dx+xydy=0?

A:

Q: Find d^2y / dx^2 when y = 8+x / 4-x

A: Simply take two times derivative of the given equation using the derivative of the form  u/v

Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

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Q: y = (ax-1) (6x.+5]%3 find dy dx 10

A:

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

A:

Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)

Q: If f(x)=3x^2 + 2y^2 =16 what is dy/dx?

A: Please see the answer below.

Q: Find the first and second derivatives. -3 y = 5x - 11x -8x dy dx d°y dx? %3D

A:

Q: Find the formula for df-1 /dx. f(x) = (1 – x)3 1 O A. 3x2/3 О В. 1-х1/3 Ос. -3(1- х)?

A:

Q: Show that dC 1.8x - 1.5 - dx Vx2+0.04 and hence determine the value of x that minimises the cost

A: if for a function f(x) at x=a ,f'(x)=0 then we check for f"(x) if it is positive at x=a , then f(x)…

Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: f cos 4x dx 2x dx S (x-2)²(x+2) x2 dx √4-x²

A:

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

A:

Q: Find d2y/dx2 implicitly in terms of x and y. x2y − 3x = 8   d2y/dx2 =

A: Consider the given function, x2y-3x=8 use implicit differentiation method and differentiate with…

Q: dx is is equal to: 2x/4-(2x)2

A:

Q: If f(x) dx = 3 and f(x) dx = 4 what is the value of %3D 5f(x) dx?

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Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

A:

Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

A:

Q: dy Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) x2+1

A: See the details solution in below

Q: d Show that In dx 1 (a) x+2 x* +3x +2 1 (b) Hence find the exact value of dx in simplest form. r*…

A: iii.a. Quotient rule of differentiation states that ddxfg=f'g-g'fg2 Chain rule of differentiation…

Q: + 2e* – 4V¤)dx , where f(0) = 7 -

A:

Q: If f(x)=3^x x^3, what is dy/dx?

A: Solution: Here  f(x)=3xx3

Q: A. Evaluate Inx dx. 2x B. Evaluate [(7x-10)dy dx. 0 x?

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: dy evaluate dx X +5 If y = %3D 2 - 2x + 3 -

A:

Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: G3-y²sinx+303")dx+ (3xy² + 2ycosx + )dy = 0

A:

Q: (x) dx = 6 and f(x) dx = 10 , then +3] dx = %3D 2

A:

Q: Chose only two: dy 1. Find for y + In x2 y2 -cos 2x* = 27 dx 2x+1 2. Evaluate: f dx -4

A: We use chain rule and product rule while differentiating the given equation.  Also for integration,…

Q: ,5. For y = 3x° - 9x° + 2x, find dx %3D dx 5

A:

Q: ution to dx = 1+t-x- dt 2 +C +C) /2-C

A: We have to choose the correct answer from the given options according to the given information

Q: Q1) Find 2/3 dx a) Jas x*/9x² – 1 V2/3

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the value of (x)) dx if f(x) dx=11 and f(x) dx=3.

A: here we have to find the integral vaule

Q: Find d^2y/dx^2 for y=2x^3-5/x^2

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Q: Find f(x)dxif 5 f(x)dx = -4 and f(x)dx = 8 f(x)dx = i

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Q: Find the antiderivate of dx/(x2+4)3/2

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Q: Sx² cos (x3 + 3) Van (x3• 3) dx + 3) Vsin (x3+ 3) dx 1)

A:

Q: .x(3xy-4y3 + 6)dx + (x³ - 6x²y2 - 1)dy = 0, when x = 2, y = 0

A:

Q: 4y2 dx = 9x2 dy when x = 4, y = -3

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.