Q.2 Let R = e2s-t2; s = 30 , t = Ø?/2 . %3D dR appropriate form of chain rule to find dø Use an

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: Find without using the Chain Rule and the ProductRule

A: We simplify the inner function using the properties of log.

Q: if y= e-e-X dy %3D Show that %3D e* te*

A: We have to prove this equation

Q: Find the denivatine.cf.tha follow.ing.vecter. Fumctanss. -j.t.In(l+3t)...k. a. e.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: for y =u dx 3/2 and u = 10x +3 using the chain rule formula dy dy du du dx Compute dx du and dx…

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Q: Q7) If y = tant ,x = tan?t at t = -! Find by using Chain Rule dx

A: We have to find derivative

Q: y = asin(k(x – E %3D

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Q: dx Q2 / Use the chain rule to find ( ) in terms of x and y dy y = ( 2 1 1, at t2 t = 2 and X t + 1.

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Q: y to solve the following linear differe ] dy

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Q: when step Qal Evaluate the x²+2Xy + y? dy dx Size of x=0,2 and step size of y= 0.5

A: We have to solve ∫01∫02(x2+2xy+y2)dydx Given step size of x = 0.2 and step size of y = 0.5

Q: H-wlo Find the dliscontinnity point of &cz):

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: The bending moment, M, varies with distance, x, from one end of a beam according to: 1 wx2 + C1x +…

A: From the given equation. M=-12wx2+c1x+c2    ....1

Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

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

Q: dy a- Use Chain Rule to find of the function below: dx y = u³, u = x? – 1 - у 3 cot u, и 3D п —-

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Consider the following. w = cos(x – y), x = t?, y = 97 (a) Find dw/dt by using the appropriate Chain…

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Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x>0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: d?x +x = secy %3D dy2

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Q: Ex 3: Use the chain rule to express in terms of x and y dx c) y = ( and x =-1 att 2

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Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x² + y? x = 5t, y = 3t t = 2 dw %3D…

A: Using chain rule

Q: Q2] Classify the following D.E to: order, degree, homogeneous, and linear: dy 2y=x 3 dx dx

A: We can solve this as follows:

Q: ら)1f u-L -*9 sin (2x ty), x = s? + 2t" and y= 2s -t" au using at find the chain rule Ond as

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Q: For a given table 2 4 6. 8 y 9. 16 23 d'y Find the value of at x = 4 using forward difference…

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Q: The volume V of a right circular cylinder of radius r and height h is V = ar?h. (a) How is 4 related…

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Q: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

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Q: Find dw/dt using the appropriate Chain Rule. w = x? + y? x = 3t, y = 10t dw dt

A: We have to solve

Q: At a website, the waiting time X (in minutes) bet ween hits has pdf fx) = 4e ", I20 Ar) = O…

A: Calculate the MGF using the formula.

Q: Which of the following plots best represents the solution with the initial condition A(0) = $1mil?…

A: Given data:   The given initial condition is A(0)=$1 million.   The initial condition can be written…

Q: (x³y³ + 1)dx + x*y?dy = 0

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Q: Find aw/@s and dw/at using the appropriate Chain Rule. Function Values .3 W =V 4, t = 8 X = e, y = e…

A: We can solve this as follows:

Q: dz at (s, t) = (0, 1) if Use chain rule to find ds "(). = e0* – st, y = s² – t2. z = 6x + y² tan x =…

A: We know that the  chain rule is the formula in derivative to compute the derivative of a composite…

Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: ;+ 2リ+y = ハ- cos(t) Slove the D- E t2 with. Ze Vo initial cuudition s En gineer ing Analysis

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Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

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Q: *?Which of the following equations Is an exact differentlal equation (x² + 1) dx – xydy = 0 2xydx +…

A: We have to choose correct options.

Q: se an appropriate form of the chain rule z = 5a*y?; x = t!º, y = t7 ter the answer in terms of t. dz…

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Q: (b) Solve the following initial vahue problem by separation of variable = 2x at x = 0, y=-2 dx

A: We will solve the problem

Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x + y 2. 2 t = 2 x = 3t, y = 4t dw…

A: Function w =x2+y2 and x=3t , y=4t To find dwdt and evaluate at t=2

Q: 5. Fied ť+, y= t*+t for t=-l equatin ef the lagest limye te the Cume an

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Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: Consider the following. w = cos(x – y), x = t?, y = 48 (a) Find dw/dt by using the appropriate Chain…

A: Here I am attaching image so that you understand each and every step.

Q: dz dz and dv Use an appropriate form of the chain rule to find du 1 = Z = e&z*y; x = vuv, Y =-

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Q: Find L ft ={fe',01 el-s -1 b. 1-s e -1 et -1 а. 1-s C. 1+s e- -1 d. 1-s

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Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: The function w=xycosz, x=t,y=t2,c=arccost. Then we have to find dwdt(a) by using the appropriate…

Q: Consider the following. w = cos(x – y), x = t2, y = 9 (a) Find dw/dt by using the appropriate Chain…

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Q: Use the chain rule to find dy/dx for th following : y= (ax+b)^5

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Q: 6 Given tthe sketch below of メ where z=x=+ y dx = -3 =-a fmin, = 1fhan; スコマ#; 4=6fe -1) スコ8#34=6€ dt…

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Q: Consider the following. w = y? - x = cos(t), y = sin(t) х, dw (a) Find W by using the appropriate…

A: Given, w = y2 – x, x = cos(t) and y = sin(t) and we have to calculate the derivative of w (a). Using…

Q: Find dwdt using the appropriate Chain Rule. Evaluate dwdt at the given value of t.

A: to find dwdt

Q: dw 3. Given w=ln (x²+y) where x=2t , and y=4-t . Find in two ways: dt (a) Using the appropriate…

A: Given:- w = ln(x ^ 2 + y) where x = 2t , and y = 4 - t . To find:- dw/dt (a) Using the appropriate…