с. у %3D (3х — 1)(2х + 5) d. g (x) — х3 — зЗx2 + 2

Q: Find the derivative of the function g(x) = 3arccos(x/2)

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Q: Find the derivative Of y=4e^-0.3t

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Q: find the derivative of y=4e^-2/t

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Q: Find derivatives of the function defined as follows. y = -4e-0.3x

A: Given,  y=−4e−0.3xFormula→ddxaex=aex  where a is constant.

Q: Find the derivative of the function 1 4. y= 4x +8x dy

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Q: Calculate the derivative of the following functions. y = cos7/4(4x3)

A: We use the power rule and chain rule to find the first derivative.

Q: Find the derivative of the function. 8y9 y= In V+9 6.

A: The solution are next step

Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

A:

Q: Find the derivative of the following with respect to the given variable 1. 2x -6x + 15x - 18 2. 5y -…

A: Solution: The objective is to find the derivative of the given functions

Q: Find the derivatives of the functions in Exercise

A: Given function is w=1z1.4+πz. To find the derivative of the functions.Solution: Power rule of…

Q: b)Find the derivative of the function by using the derivative definition? ds if s dt 2t + 1

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Q: Find the derivative of the function.

A: Consider the provided function, ht=t2t3+22 Find the derivative of the function. Apply the chain rule…

Q: Find the derivative of the function y = coth 8x2

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Q: Find the second order derivative of ycos³(2x).

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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: Find the derivative of the following functions without skipping steps y = - cos ? (3x) + ctg² (5x³)…

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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: 1. x + y + xy = 21

A: We will use simple differentiation rules to solve this question.

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). h(x)=…

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Q: suppose that x and y are related by the given equation and use implicit differentiation to determine…

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Q: Calculate the derivative of the following function. 4x y = e **(4x- 1)9

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Q: suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: Find the derivative of y = arccos 4x with respect to x. - 4 4 а. b. 1-4х* V1-4x? - 4 - 4 с. d.…

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Q: 1 f(y) = y² )(y + 5y³) y4,

A: let us simplify function firstf(y)=(1y2-1y4)(y+5y3)=(y2-1y4)(y+5y3)=y3+5y5-y-5y3y4=5y5-y-4y3y4it can…

Q: Find the derivative of the function. y = 7xe−kx

A: Differentiate both sides w.r.t xUse product rule on the right side.

Q: -1 y = cos –6•x³ - 6·x³

A: Given function is: y=cos-1-6x3 Then we get, cos y=-6x3

Q: Find the derivative of the function. 76 y = Vx - X y' = O

A: We know ddxxn = n·xn-1 xab = xab x-a = 1xa

Q: 2x+5 e. y = 3x-2 f. y = (2x? + 2)(x² + 3)

A: Derivative of the function y=f(x) is the measure of rate of change of y with respect to x.…

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: 5. y³ = 4(y + x²)

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Q: Use the rules of differentiation to find the derivative of the function.                y = t2 − 3t…

A: Differentiation: y=t2-3t+1Derivative of the function we need to find out.We knowddx(xn)=n.xn-1

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 derivative of the following: 1. y=x(VT- x³)

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Q: Find the derivative of the following e^2x y = π / 2 y=5e^3x

A: Given function, y=e2x Using the chain rule of the derivative y'=dydududx Let 2x=u The derivative of…

Q: Find the derivative of the function. G(x) = V1 - 9x² arccos(3x) G'(x) -

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Q: Find the derivative with respect to x: y = x3- 3*

A: The given function is: y=x3.3xWe need to find the derivative of y with respect x.Recall the…

Q: Find the derivative of the given function y = (2x+ 5)v4x – 1

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Q: Find the derivative of the function y = x2x+1

A: We have to find derivative of the function: y=x2x+1  In this situation we use logarithmic property…

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: Find the derivative of the function. G(x) = V1- 9x2 · arccos(3x) G'(x) =

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Q: Find the derivative of the following function. f(z) = (4z+ e -)*

A: As we know that ddxex=ex [ common derivative]ddxe-z2 =-2e-z2 .z

Q: Solve for the derivative of the following Exponential Differentiation. 1. y = 92x^2 + 3x +1 2. y =…

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

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Q: Calculate the derivative of the following functions. y = sec (3x + 1)

A: Given:  y = sec (3x + 1)

Q: Calculate the derivative of the following functions. y = (5x + 1)2/3

A: The given function is: y = (5x + 1)2/3 The chain rule is: ddxfgx=f'gx·g'x And, the derivative of xn…

Q: Find derivatives of the functions defined as follows: y = 4e2x2-4

A: We have  y=4e2x2-4 Then, dydx=d4e2x2-4dx=4de2x2-4d2x2-4.d2x2-4dx=4e2x2-44x=16xe2x2-4

Q: Find derivatives of the functions defined as follows: y = -4e-0.3x

A: Our Aim is to find the derivative of the function given below:-y=-4e-0.3x -(i)

Q: Find the derivative of the function. 4x° +8 y = y' =O

A: We have to find

Q: Find the derivative of the function. h(x) = ex + 5

A: First we will differentiate exponential part then we eill differentiate algebraic part

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: