Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

Q: 9)/6)= (2x+1)*

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: In the given question/s, use implicit differentiation to find dy/dx.:-   ln xy +5x = 30

A: Since the equation lnxy+5x=30 is given in two variables, use implicit differentiation to calculate…

Q: Use logarithmic differentiation to find dy/dx.

A: To find dydx:x2-3lny+y2=0 Solution: Given equation is: x2-3lny+y2=10 Differentiating both sides…

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

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Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: 91. Use implicit differentiation and the fact that (x) =. .2 dx and (r5) = 5x4 to prove that (x3/5):…

A: Consider y=x35. Now y5=x355=x35·5=x3⇒y5=x3 . . . . . . . (1)

Q: If f(x)=In(x-1), find the formula for f^((n))(x), the nth derivative of function f(x) f(x) = ln (x –…

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Q: Find the first derivative for each in the form of dy/dx   1.)  y= 3root(x^2)- 3/x^3 + e^ -5x +…

A: Explanation of the answer is as follows

Q: Find the implicit differentiation by using Total Derivatives a function, x³ cos(2y) – 3x4 + 2e³y

A: Given problem:- Find the implicit differentiation by using Total Derivatives a function,   x3…

Q: Compute the following derivatives. Use logarithmic differentiation where appropriate.

A: Given function is fx=2x2x

Q: Find by implicit differentiation, and evaluate the derivate at the given point. dx 3. x - y = 0 at…

A: 3) x3-y2=0 at -6, -14) x+y3=x3+y3 at -1, 1

Q: D. Now use implicit differentiation to find +(In y).

A: Given : (2D) y = x2πx

Q: 3. Use properties of logarithms and/or logarithmic differentiation to find the indicated derivatives…

A: a.)  y =ddxlnx2   ⇒y =2ddxlnx =2x                                                  ln(ab)…

Q: Solve the following using the formulas used in Differentiation y = - 4 x3 y = 4Vx5

A: the given function is y=-4x3 use the formula d(ax)dx=adxdx ddxy=ddx-4x3=-4ddx1x3=-4ddxx-3 use the…

Q: Find an expression for the derivative of h(x)=ln(f(x)). answer in terms of f and f'.

A: The given function is  h(x) = ln(f(x))

Q: Find the following derivative In (x) dx 3 In (x) + 4 In (x) dx 3 In (x) +4 d. 이증

A: Formula

Q: 1. D, (x') 2. D, (5x) 3. D. (x-2x)

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Q: Find the derivative of each function h(x) = 2x³ In x h(x) = 6e*(1 –- 5x) g(x) = 3 sin x cos x + 2x…

A: Given, The functions  hx = 2x3 lnx  hx = 6ex1-5x  gx = 3sinx cosx +2x  We have to find the…

Q: Find the following derivative. (4* + 8) In x) dx

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Q: Find by implicit differentiation, and evaluate the derivate at the given point. dx 4. x3 - y? = 0 5.…

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Q: Find the derivative of f(x) = ln (x* /8 – 6x), using the properties of the logarithm. Provide vour…

A: We will find the derivative of the given function f(x)=lnx48-6x by using the properties of logarithm…

Q: Use the method of implicit differentiation to solve the equation for dy/dx: x^3y^2+1 = 2xy

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

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

Q: Find the derivative of   n^[ ln(cos u) ]  . Where n = 744

A: We will use logarithmic differentiation and chain rule of differentiation to find the derivative of…

Q: 4 f (x) = 3 (In (9x² + 7(log5(+Vx*

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Q: Use logarithmic differentiation to find dy/dx for y=5√x-1/x+1

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Q: x coSx dx =x sin x + cosx+ C %3D By using the differentiation, verify that the given formula is…

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Q: Use the Intermediate Value Theorem to show that  there is a root of the given equation in the…

A: Given : ln(x) = x - sqrt(x) , (2,3)

Q: 8. Find the derivative of (logsx?). dx 2 A. x In 5 1 В. x In 2 С. x In 5 D. 2x In 5

A: Solving the problem by finding the value of the derivative. For the question no 8. Option A is…

Q: Use logarithmic differentiation to find dy/dx.

A: ln(mn)=ln(m)+ln(n)lnmn=ln(m)-ln(n)ddxln(x)=1x

Q: Find the following derivative In (x) dx (In (x) +2) d In (x) dx In (x) +2 d

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Q: Use the technique of log differentiation to find when y = (sin(x))In(x) %3D dx and then evaluate it…

A: Given that y=sinxlnx find dydx using log differentiation

Q: d Use implicit differentiation to prove that x"| = nx"-1 dx

A: Implicit differentiation is a method to solve the differentiation of an equation without the need to…

Q: (т3 + 5) e2x /2x – 1

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Q: Find by implicit differentiation, and evaluate the derivate at the given point. dx 4. x - y? = 0 5.…

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Q: Find the following derivative In (x) dx In (x) +2 d In (x) dx In (x) +2 d 이종

A: NOTE: Refresh your page if you can't see any equations. . use the quotient rule for derivatives

Q: Verify by differentiation that  ∫ ln x dx = x ln x - x + C.

A: The given statement is ∫ln x dx=xln x-x+C. Verify this as follows.

Q: i dont understand a) through c)

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Q: Find the indefinite integral and check the results by differentiation? (4x^2 + 3)^2

A: I=∫(4x2+3)2dx =∫(16x4+24x2+9)dxintegrateI=165x5+8x3+9x+c    where c is any constant

Q: y = log4 x %3D .y = In(5x2 -4x + 8) %3D

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Q: 7e e*²-sin(2x) sin(3x)sin(4x)

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Q: Use logarithmic differentiation to find dy/dx. Do not simplify the result. (3x + 1)2 y = 6x(2x – 1)3…

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Q: Use logarithmic differentiation to find y = (In x) sin, x> 1. dy dx given

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Q: Use logarithmic differentiation to find y′, given y = e2x xx √(x3 + sinh(3x))

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Q: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: Determine whether each of the following statements is true or false, and explain why:The derivative…

A: The given equation is derivative of ln kx  is same as the derivative of ln x

Q: 2. Use the logarithmic differentiation to simplify completely before finding the derivative.…

A: As per our company guidelines we are supposed to answer ?️only first question. Kindly repost other…

Q: Use logarithmic differentiation to find the derivative of the function. e y = cos?(x) 2 3x2 + 8x + 9…

A: Here , We will find the derivative of the given function using logarithmic differentiation.    We…

Q: Solve the following using implicit differentiation.     sqrt(x+y) = y2 + x2

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Q: arc sin z = -i log(iz + V1- 22).

A:

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: