determine whether the following statements are true or false  1. if z=f(y) and y= g(x) then dz/dx= dz/dy X dy/dx  2. if A=B (both positive) then ln(A)= ln(B) and vice versa.

Q: Зx + log dy find dx If y = 4 — Зх -

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Evaluate dx dy in y=cosh(in e") b. 3x sinh (In x') 3x² sinh(In e* ) d. 3x sinh (3x² ) с. a. 3x…

A: Given:     y = cosh ( ln ex^3 )

Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Q1) Answer the questions by true or false 1) If y = In then the derivative of y is = (x2 + 3) * 2x…

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Q: Use x = ey to explain why d/dx (ln x) = 1/x, for x > 0.

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: f(x, y) = log, (3x) fe dy In(3x)/(yln(y)2)^2 ||

A: Topic- partial differential

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) x2 if a = 323 and b = 0.5 at x = 3 using…

A: Given function is f(x)=323cos0.5xx2 Step value is ∆x=0.1

Q: Given e^x - x^2 + y^3 = xy, find dx / dy using implicit differentiation

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Q: Find dy / dx, using implicit differentiation. exy = 7 dy dx Compare your answer with the result…

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Q: e (sinh x dx + cosh x dy) = 0

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Q: Find the equation of the line tangent to xe^1−x at x = 1 and x/e * ln x at x=e.

A: To determine the tangent lines to the curve using derivatives

Q: 51. The functions y = e* and y = x³e do not have elementary anti- derivatives, but y = (1 + 3x)e"…

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Q: Can i get help step by step please

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Q: Can you help me with this problem step by step?

A: Given that

Q: In the given question/s, find dy /dx by implicit differentiation :-   x2 + y2 = 9

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

Q: Let e - v = 1. Find each derivative. du dv (a) dv (b) du (c) Based on your answers to parts (a) and…

A: eu2-v-v=1

Q: 1. Calculate dy da for the following: (a) y ln(x + 2x³ - 6), =

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Q: Evaluate the second derivative of e22.1.png а f(x) acos(b/x) x2 if a = 345 and b = 0.6 at x = 5…

A: Given: Let us consider the given, fx=acosbxx2 where a=345 & b=0.6 at x=5 using BDA with ∆x=0.06.…

Q: 2. If y = x +3x-2x+1, find the values of the following e. derivative, i. У"(2) d'y ii. dx ii. y" (2)

A: Please refer to the image below

Q: 2. In each case, find the derivative d (a) z = x* + y and r(t) = In (t) and y(t) = e24, (b) z = 5xy…

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Q: Find the derivative of y with respect to x. y = sin (e 5t) e 5t e OA. 1- e 10t 5e 5t O B. 1- e 10t 5…

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Q: 44. Solve for the second derivative of y = e5x а. 25е5x b. 25e4* c. 25e3* d. 25e2x 45. Find dy/dx of…

A: NOTE: Refresh your page if you can't see any equations. . take derivative take the second…

Q: 1. Applying the definition of derivative, a. find dy/dx in each of the following: 1 a. 1] y = - x² –…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: 大 If x < 0, which of the following has the derivative 1 dy (1 – a)Va - 2a =? dx |3|

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Q: Find dy for the given values of x and Ax. 3 2 y = x° - 3x + 5; x = 1; Ax = - 0.1 What is the…

A: Given: y=x3-3x2+5 ; x=1; ∆x=-0.1

Q: Take the derivative of the following: Dy= 3xe y = e (3) e y = @y= In () 10 Y=ln (In x)

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Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: Let y = (x° – 15a)m(@). Find dy using the method of logarithmic dx differentiation. Express your…

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Q: Find dy for the given values of x and Ax. y = x° - 5x + 5; x = 1; Ax = - 0.4 What is the derivative…

A: Here, the given function is: y=x3-5x2+5

Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: Can you help me step by step with this problem?

A: To compute the derivative of the function.

Q: 2. 2メ dy dx for y = Cos (ln x + e put lに

A: y = cos2(ln(x) + e2x)

Q: Given that y = (In(x))²In(), find dy using the method of logarithmic d.x differentiation. dy %3D

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Q: Find the differential of the function. = e dy =

A: y= e^(2x) dy = 2 e^(2x) dx

Q: Find dy/dx using implicit differentiation: xe^y − y^2 − x^2 = 2 and Find dy/dx using logarithmic…

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Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: Evaluate the second derivative at the given point. dy If dx = 3 ey + x2, find at (4,0) dx2

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Q: Find dy/dx by implicit differentiation for the following.:x + ln y = x2y3

A: The given equation is x+ln y=x2y3. Compute the derivative as follows.

Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: 2. Find the following derivatives. (a) y = log; (xe*Y loz Leet (c) y = 38z2-5 (e) h(v) = e-2"…

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Q: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

A: Given data is: z=lnx8+e5 To find the value of dzdx

Q: 3 dy Find dx if y = cos vx + 4sin x – log 3(3x + 1)ž. إضافة ملف

A: We will solve the following

Q: Find the derivative of y with respect to x. y = sin -1(et) OA. 5e 5t /1- e 10t O B. - 5 e 5t /1- e…

A: We have to find

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: