Calculate dw/du and ðw/dv using the following functions: w = f(x,y, z) = 3x² – 2xy+4z² - x = x(u, v) = e“ sin v y = y(u, v) = e“ cos v = z(u, v) = e".

Q: Let r(t) = (sin t, 2 cos t), t = (a) Find r'(t). (b) Find T(t).

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A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

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Q: find dy Say y=3 Sin 8)

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Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²* sin(5y)j + z5k. f(x, y, z) =

A: The given gradient function

Q: Calculate dwldu and using the following functions: = f(x, y, z) = 3x2 – 2xy + 4z2 x(u, v) = e" sin v…

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Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

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Q: Y : = x COS -1 x – V1 - x2

A: Given function :

Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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A: Given equation: y=cosxxsinx

Q: dy b) Find dx Y=cot4 (sinx) XU

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