Determine y' of y = V4x+3

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

Q: Find the points where the tangent line to y =2+4 is horizontal (Critical points)

A: We need to find points where the tangent line to y=xx2+4 is horizontal. In other words, we need to…

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: Find the first four derivatives of y = 4sinx. %3D

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Q: 5. Find the equation of the tangent and normal line of 2x+1 y = at point (1,1). x+2

A: A detailed solution is given below     (As per our guidelines, we have to solve only one question)

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

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Q: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: Find equation of tangent y=x³-4x+1 at point (2,1)

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Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: Find dx at x--3 if y-5x-2 and Do NOT Round.

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Q: Find the general solution of y'= sin²xcosy.

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Q: Calculate the derivative: + (2t3 – 9t) dt = dz

A: Evaluate the given derivative as follows. ddx∫0x2t3-9tdt=ddx2t44-9t220x=ddx2x44-9x22-0

Q: Find dy/dx at the point (2,1) if 4y3-x2y2=0

A: Given that: 4y3-x2y2=0

Q: Differentiate: F(y) (y + 9y°) yA - y?

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Q: 5 Calculate the second and the third derivative of y = 6x – y": y"

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: what is the partial derivative of 2=Yytylnlxy

A: Given query is to find the partial derivatives.

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

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Q: Find dy/dx at the point (2,-2) if 3y2-4x2+4=0.

A: Find dy/dx at the point (2,-2) if 3y2-4x2+4=0.

Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Find both first partial derivatives. az

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Q: TO Show Jv - x-V そーレ V+ dx

A: Jvx = ∑m=0∞ -1mx22m+vm! m+v!

Q: Find the partial derivative. z = sin (6

A: We have to find

Q: у %3D V1+ 2х (1 — х)-3

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Q: 6) Calculate - dx for z = ln(x + y²).

A:

Q: Find the equation of the tangent and the nirmal to the curve y=5x4 at the point (1,5)

A: Given curve,  y = 5x4  To find the equation of tangent and normal at the point (1, 5)

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

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Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: Determine the derivative of y. y = eV14x+6 %3D

A: Please refer the attached image for complete solution.

Q: Find the equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: A) Differentiate y = 4Vx +- +1 8 6 B) Find the second derivative of y = 4Vx + 8 + 10 Vx

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Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: ential equation is given by

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Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Given: y=∫x22x2lnt dt

Q: ry' = 3y + y? ху

A: Solution of a nonlinear differential equation

Q: y 1-

A: The solution is given below in the next step:

Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Q: Compute the derivative y = dy %3D dt 2t - 7 y = 7t- 3

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Q: What is the integrating factor of y' - 2xy x?

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Q: Find the equation s for the perpendicular trajectories of the curve family. 1. x -

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