Let h (z) = fi v (2t) dt.Find h' (1). Show the computations that lead to %3D your answer.

Q: If y = 2x^2 - 3x and dy/dt = 3, find dx/dt when x=2.

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Q: 1-dt 3- Ln(t) dt. Q10:- Calculate dx J2x t2

A: Use fundamental  theorem of calculus

Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: Which of these gives an integrating factor for dy 2ty = 3t + 1 dt -

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Q: Find the differential d5y of the function y=sin2x.

A: To Determine: Find the 5th differential of the given function y = sin(2x)

Q: If y=x^4−5 and dx/dt=−1, find dy/dt at x=−3.

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Q: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

A: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

Q: Find the total differential. z = 10x"y3 dz =

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Q: Find the total differential dz ZzxeX+y

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

Q: Find dy/dt if y = tan^−1 (1 /√t)

A:

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: This is a linear DE. If arranged to its form, what is the integrating factor? * xdy ニ

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Q: find the integrating factor (x+1)dy - (2y+2x+1)dx = 0

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Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: Find the derivative of the function y = In(3t + 4). %3D dy dt

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Q: Let xy = 3 and dy/dt = 4. Find dx/dt when x=2?

A: Given :                xy = 3  , dydt = 4 To find :                      dxdt when x=2

Q: - (v + x³ + xy®)dx – xdy = 0.

A: To solve the given differential equation.

Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

A: Note that velocity is rate of change of displacement. Hence displacement will be integration of…

Q: ,dz Find ifz = xy2 +x²y, y = ln x - dt

A: We are given : z=xy2+x2y and y=ln x⇒z=x(ln x)2+x2 ln x

Q: Let xy = 1 and dy/dt = 3. Find dx/dt when x = 1?

A: Consider a function u(x) such that, Now, according to chain rule,  The given information is,

Q: The integrating factor of 3xdy + 3y dx is

A: given differential equation: 3xdy+3ydx=0 Remember :  A differential equation of the form…

Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA dx

A:

Q: 5) If y = x³ + 2.x and dx/dt = 5, find dy/dt when x = 2.

A: Q.5) If y=x3+2x and dxdt=5 Find: dydt when x=2

Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: What is an integrating factor of the DE dy/dx = (y + y^2) / x ?

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Q: If 3xy+x^2=7 and dy/dt=-16, find dx/dt when x=1

A: Derivative, in mathematics the rate of change of a function with respect to a variable. Derivatives…

Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: Find the indicated derivative. dy dt - for y = (2.2t - 4t?)(2t + 1.9) dt 11

A: We have to find dy/dt for Given function.

Q: If x ^2+ y^2=100 and dy/dt= 4 , find dx/dt when y =6

A: Solving the problem by method of differentiation.

Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: Assume that 2x + 3y = 12 and dy/dt = -2. Find dx/dt.

A: Assume,

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Calculate cln 2 I = Ver – 1 dx thanks to the change of variable u Ver – 1. U = -

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Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: Suppose xy=−4 and dy/dt=1. Find dx/dt when x=-1.

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Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: Find dy/dt Y=(1+Sin 12t)^-5

A: Given function is y=(1+sin12t)-5

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

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Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

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Q: zp dt

A: we have to solve the differential equation. dzdt+2et+z=0

Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

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Q: Find the integrating factor of (x² - y²)dx + (x² - 2xy)dy = 0

A: Given  (x2-y2)dx+(x2-2xy)dy=0

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,