Let w(z, y, z) = 1 + y² + z?, where z = 3', y = Int, and z = = et. Find I using the Chain Rule.

Q: Let f (L, K ) = 32LK. Find df/dL.

A: Differentiate the function f with respect to L.

Q: did u get C1 , C2 and C3 for the intgrating constant

A: Given:- How did u get C1 , C2 and C3 for the intgrating constant.

Q: In(t – 8) 5 7t3 b. y= | 8t

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Q: Find ▼ × (V × F) if F(x, y, z) = 6xyj+xyz k. V × (V × F) =

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Q: If f(r, v) = ry – ry", find 7 + ±),-.y-a

A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

Q: Let w = x? dx + y? z² dydz. Find dw.

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Q: The integrating factor of the equation (xlnx)y' + y = 2lnx is || Select one: a. ex O b. Inx c.…

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Q: Determine the order of the DE. a.) y' + y = 5y^2 b.) (dy)/(dt) = t c.) y' = y'' + 5t^2

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Q: Let v = (2, (2, 3, 2) 3,

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Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

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Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: Find the FT of the Rectangular of width T and compare Pulse with the FT of rect (t)= g(t) = Areet…

A: Definition:

Q: Find (r.)ifr=√.e and r₁=(. In (21)) r, dt

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Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

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Q: 5-find Аху : xe 12) if f(x, y) = xe

A: First I have mentioned what we have to find then just use the rule of partial derivative find the…

Q: Find u · (v x w). u = (4, 0, 0) v = (9, 9, 9) (0, 4, 4) w %3D

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Q: Find dy/dr. y = In(re")

A: Given To find Derivative of y= ln(xex)

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: Evaluate S xy dx + (x + y)dy along the curve y = 2x² from ( − 3,18) to (-2,8). с Sxy dx + xy dx + (x…

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Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: Differentiate. V(t) = (t + 7e')/t %3D 3 7/)eIn(e) + v7 * V'(t) = 2

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Q: Show that A Yk= V' Yk+r

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Q: OLif f(x, y,z)=2exp(-5xyz)cos(15z) Find

A: Partial derivatives

Q: f (x,y) =x³ cos y Given df (2, 1) дх of and (2, л). Evaluate ду

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Q: Use a substitution of u = r to integrate : dr.

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyz

A: Given fx,y,z=e-xyz Partial derivative means differentiating with respect to one variable keeoing…

Q: (b) Calculate dx ds ду ds dz ds II || ||

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Q: Suppose X - Uniform (0,1). Find the CDF and PDF of Y = InX.

A: To find the cumulative distribution function (CDF) and probability density function (PDF) of the…

Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

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