Using the definition of a derivative, what is y'(z) given that y(z) = z* +z² – 5z +3? (Do not include "y'(z) =" in your answer.)

Q: dy Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y³. dx

A: Given that: 3x2 +2xy = -4y3. Find dy/dx. We know that derivative of xn is nxn-1.   Here i attached…

Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: 3) Find the second derivative of y with reference to x. xcosy = y

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Q: Find y’ if y=cos(ln(x^2 +1)) y’(0)= Use implicit differentiation to find the equation of the tangent…

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

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Q: Find the derivative of the function. y = esin(5x) + sin(e5x) y' =

A: The solution are next step

Q: 1-x Find the derivative of y = arctan %3D 1+x

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Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: Find the derivative of function.

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Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: , find the derivative of y with respect to the appropriate variable 21. y = ln cosh y - 1/2 tanh2 y…

A: (21) Consider the provided equation, y=lncoshy-12tanh2y Find the derivative of y with respect to the…

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Find the derivative of y with respect to x. y= 3x^3 sin^-1 x show all work

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Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

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Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

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Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: Find the derivative of y with respect to x. -1 2х + 3 26) y = sec" 27) y = -sin-1 (5x2 + 2) 28) y =…

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Q: Find the derivative of y with respect to x using implicit differentiation in the equation *'y =…

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Q: find the derivative of y with respect to the appropriatevariable. y = 6 sinh x/3

A: Given function: y=6sinhx3 Using the common differentiation of hyperbolic function: dsinhaxdx=acoshax

Q: Derivative of y with respect to x

A: taking logrithum both sides and solve the question.

Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

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Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

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Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: Using central difference, find the second-order derivative of y=x²cosx at x=9, h=0.1

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Q: Find the derivative of the function using chain rule. f(x) = esin?x

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (2e-tsin t)

A: On simplification, we get

Q: What is the second derivative of y = 2x -+ sin x with respect to x? a. 2 -+ cos x b. 2 ++ cos x -+…

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Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: Find the derivative of the function using implicit differentiation.  1.) x²y + y²x = -2  2.) √(xy)…

A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

Q: N= cos(5x) (SX メコ

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Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: the Chain Rule.

A: Given: y=11-x46. Let, u=1-x4 By chain rule, the derivative of y with respect to x is given as,…

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y 1- 6 sinh || 1 y sinh (2x + 1) 2-…

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Q: 1) Find the 3rd derivative of y = sin(x) %3D

A: To find the 3rd derivative of y=sinxx. Solution: For finding third derivative, we need to find first…

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 dy dx b) EVALUATE THE DERIVATIVE FROM PART a AT THE…

A: Given: x4y3=-8

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: 2- Find the derivative of y with respect to the Exercises 1-3. = 6 sinh 1- 1 sinh (2x + 1) 2- In…

A: These are the hyperbolic function so use standard form of derivative of hyperbolic functions.

Q: The second derivative of an anti-derivative of a differentiable function F R-R is: O possibly…

A: The second derivative of an anti-derivative of a differentiable function f:R→R is

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

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Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

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: