1. Find the average rate of change in y with respect to x over the interval [1, 7]. 2. Use the definition to find f'(x) and then find the equation of the tangent line to f(x) = v4x – 3 at x = 3.

Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

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Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: 1. Find the rate of y with respect to x at the point (1, 7) if 7y – ry = 4. dy da

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

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Q: Find the derivative of y with respect to t. y = In (4te 8t) dy

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Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: Find the value of the derivative of ƒ(x, y, z) = xy + yz + xz with respect to t on the curve x = cos…

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Q: Find the derivative of y with respect to x. y = In (x) dy 8. dx %3D

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Q: Find the derivative of y with respect to x. y = 9 In (6 In x) dy %3D dx

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Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

A: Given query is to find the derivative of the expression.

Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Determine the equation of the tangent line to the graph of g(x) = mz [1 – sin(ne')]dt at the point…

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Q: Find the derivative of y with respect to t. y = tan - 1 2t V 2t dy dt

A: We have to solve

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: Consider J(0) = 30* + 1. Let e = 0.001, compute the numerical approximation to the derivative at 0 =…

A: The given problem is to find the derivative of the given function at point 2 with given accuracy…

Q: Find the derivative of y with respect to 0. y = In (8 cos 2e) dy %3D de

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Q: Can i get help step by step please

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Q: Find the derivative of the following functions without skipping steps w = 7x sin (z?) – z? sin (y) +…

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Q: 6. Suppose that w = x cos(yz²), where x = sin t, y = t² and z = 2e'. Find the rate of change of w…

A: Using derivative

Q: Suppose L is the tangent line of f (x) = csc T at x = 2 . Where does L intersect the y-axis? Note:…

A: We have to find

Q: Find the average rate of change of f(x) = x2 + 3x + 1from 1 to 2. Use this result to find the…

A: Average rate of change of a function f(x) is calculated as the total change in the function divided…

Q: Find the total derivative of the function f(x, y, z) =+z In (2x+1)+sin (xy) xz

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Q: Find the derivative of the function. r sin(x) y = Jcos(x) In(4 + 9v) dv y'(x) = %3D

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

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: find the derivative of y with respect to x, t, or u,as appropriate. y = e^(cos t + ln t)           .…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: H.W: Use the chain rule to find the derivative of w= x² + y² with respect to t dw dt with x = cost +…

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Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

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Q: Find the derivative of y with respect to t. y = t(In 1t)2

A: The given function,  y=t ln 1t2

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Q: Find the derivative of y with respect to t. y3 t(ln 10t)2 dy dt

A: we have to find derivative

Q: b) Find the value of the derivative of f(x, y, z) = xy + yz + xz with respect to t on the curve x =…

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: I. Determine the equation of the tangent line to the graph of f(x) V3+ 5t5 dt at I= 1.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: Compute the derivative of h(sin(x)) at x = T/6, assuming h'(0.5) = 10:

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Q: Find the derivative of y with re Ind the (x* In x) y = dy dx II

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Q: Find the value of the derivative of g (x, y) when we restrict to the curve defined by x = cos t and…

A: Differrtiate with respect to t

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Q: Find the derivative of y with respect to T Y=t(ln 4t)^2 dy/dt

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Q: The slope of the tangent line to the graph of y = ln x at x = a E R approaches infinity as a → 0+.

A: Given curve: y=ln x

Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: H.W: Use the chain rule to find the derivative of w = x² + y² with dw respect to t dt with x = cos1…

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Q: Can i get help step by step?

A: We take ln on both sides and use logarithmic differentiation. Using the product rule and power rule…

Q: The derivative of the function y = cos VI at z = is equal to 4

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

A: Given data is : dxdt=5et-3 , x0=4 To find the antiderivative

Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

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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: