Calculate the derivative of the function below using the quotient rule. 28 y = Vx + 8x7 f(æ) = %3D and g(æ) = which means that f'(x) = and g'(x) = %3D And thus 28 Va + 8x7

Q: B) Find the third derivative of the function: Y = + VX3 %3D

A: We have to find third derivative

Q: Find the derivative of the function. y = (lnx)        (x7)

A: Quotient rule of differentiation:If a function f(x) is a quotient of u and v where both u and v are…

Q: Find the derivative of y = 6x°e* + 3x° y' =

A: Given data is : y=6x3ex+3x5 To find the value of derivative y' Formula of differentiation…

Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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Q: Find the derivative of y with respect to x. 4. (x² - y²)² = 4ay²

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Q: Evaluate the derivative of the function at the given point. 1 y = 7t + 1 = - 1

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Q: calculate the derivative with respect to x. y−2/3 + x3/2 = 1

A: Given: y-23+x32=1 Taking logarithm on both sides of the given equation, logy-23+logx32=log1…

Q: 5. y= 2arctan(vx)

A: We need to evaluate the derivative of the following function y = 2arctanx

Q: Evaluate the derivative of the given function for the given value of x. Y = 2x-3 / 4x+5   x = 1…

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Q: Find the derivative of the function. 4x +6 y-D y'3D

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Q: 2. Calculate the derivative by first principles for the following: i. f(x)=Vx,

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Find the derivative of y with respect to x if y = (13x - 26x+26) e -8x y =D %3D

A: Explanation of the answer is as follows

Q: 2. For y = 6x*V4 + x, find y(2).

A:

Q: 6. Determine the derivative of the function with respect to x. y = x2 – V2x +1

A: Solve the given problem.

Q: What is the derivative of y = e2 +1, with respect to x?

A: Formula used

Q: Find the derivative of the function y=2x+12x−1 at x=1.

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Q: Calculate the derivative of the following function. y=V19x - 8

A: Given,            y=19x-8To find : Calculate the derivative of the given function.

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: Determine the 3rd derivative of the function y=x3/x+2 at x=−1.

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Q: Find the third derivative of the function: Y = =+ VX3 %3D

A: To find the third derivative of the function: y=1x+x3

Q: find the derivative of y with respect to the givenindependent variable. y = 3log2 t

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Q: Find the derivative of the following using the three-step rule Зх — 1 1. y= 2х+5 2. y=Va? +x?

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3 2x +5 2. y=Va² +x?

A: Using three step rule.

Q: Find the derivative of the function y=(x−1)(x−2)(x−3) at x=0.

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

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Q: The derivative of the function y = x² In(x + 1) is:

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

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Q: Find the first derivative of with respect to x using the increment method y=3x^2-7x+12

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Q: Find the derivative of y with respect to x. x7 x7 X' Inx- 98 y = 14

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Q: Find the derivative of y with respect to x. 1. x² + 4y² = 4ay

A: Given:   To find: Derivative of y w.r.t. x:

Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

Q: (x²+7) Yキ 7. フーX

A: We use first derivative devide rule and differentiate of y . Here i provide full solution of this…

Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. In x 20) у 3

A: Given

Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

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Q: find the derivative of y with respect to x, t, or θ, as appropriate.

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Q: y = V5х+7

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Q: find the derivative of the following function x2y= (y+2) + xysin(x)

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Q: Find the derivative of the function. y = 3x 8 * - 12x - dy dx II

A: Explanation of the answer is as follows

Q: y= 4x2-2x - 3

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Q: Calculate the derivative of the following: y = Vx + 4

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Q: Which is the first derivative of y=vx ?

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Q: find the derivative of the given function y^4=4xy using implicit differentation

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Q: Find the derivative of the function y = csch−1 (1 − x)

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Q: 10. Find the derivative of y with respect to x. y=(x^(6)lnx)^(4)

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Q: Find the derivative of y with respect to x. 3. (x² + y²)² =ay²

A: The equation given to us is

Q: Find the derivative of the function: f(x) = Vx + Vx + 1 1 +

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Q: Which is the first derivative of y=vx ? *

A: Given Data: y=x Formula: d(xn)dx=nxn-1

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: