Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y = (3x + 5)/ x^2 - 4x + 2 3. y = x^2 sin(3x)

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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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: 3 y (sinhx) + sinhx 3 4. step1 step2

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Q: find the derivative of y with respect to the appropriate variable. 1. y = cos-1 (x2)   2. y =…

A: Part 1. Given,

Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. xy = 24,…

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Q: what is higher order partial derivative and total differentials?

A: We have to define given Terms.

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: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: Use the derivative rules to write the first step of differentiation. (arctan(x))6 = 6 (arctan(x))5 ·…

A: We will find the first step of differntiation as following

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

A: We have to find the second derivative of the following function at x=-2 with step size h=0.5 using…

Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Find y' by implicit differentiation 1. x²+4x-3y²+4y=0 2. 2xy+π sin y = 2π

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Q: Find dy/dx using appropriate derivative rules. (don't simplify) 1. y=sin^-1(x^4) 2. y=…

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Q: Find the Indicated Derivative for Higher-Order 1. y = 10x5 - 21x4 + 13x3 - 6x2 + 5x - 1000 ; y(6)…

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Q: by implicit differentiation. dx Find - (5x + 2y)1/3 = x2 dx

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Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: find derivative       1. y = ln 3x + x    2. y = ln (t2)    3. y = ln (3/ x)    4. y = ln (u + 1) -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the derivatives of the functions in Exercis

A: Chain Rule: f(g(x))'=f'(g(x))g'(x) Differentiation formulae: ddxsinx=cosxddxcosx=-sinxddxax=a

Q: 8. Find the derivative of y = x arctan 2.x --In(1+4x). -- - 4.

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Q: what is the partial derivative of 2=Yytylnlxy

A: Given query is to find the partial derivatives.

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

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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: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: implicit derivative to find dy/dx of    xy + arcsin(y)+2^y=ln(x)

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Q: 7 dy if Use implicit differentiation to find 8. dx dy dx +

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Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: Find the second derivative of y = (4 – 2x)2 + 2sinx. dy Directly type your answer WITHOUT y' or dx…

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Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

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Q: Find the derivative of fcx) = en (sinh Cx)) 5

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Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: Calculate the partial derivative * using implicit differentiation of exy + sin (3xz) + 2y = 0. (Use…

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Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

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Q: Find the first derivative for each in the form of dy/dx  show all work please   3.)…

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Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

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Q: Compute the derivative ln(ex+1) / 2x+1

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Q: find implicit derivative dy/dx of x2sin2(y)+2x2=y

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Q: Find the derivative of: sin sin(2x) sin sin(x) + cos (2x) cos(x) ans: -sinx solution?

A: We will use the formula cosA*cosB+sinA*sinB= cos(A-B) , with A=2x and B=x and simplify.

Q: Find dy/dx by implicit differentiation at point (0,-2) if x^3-xy+y^2=4. O -2 -2/3 1/2 3/4

A: Implicit derivative at point

Q: Find y'' by implicit differentiation. 5x2 + y2 = 4

A: Implicit differentiation

Q: Find the fourth derivative of the given: (Show complete solution from first to  fourth derivative)…

A: The function is given by y = (2x+1)25

Q: Y = 2 Arccos ( 1 -) + v4x – x²

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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: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.