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25 = d. Assuming f(w, x,y) (6w+1) cos(3x² + 4xy³ + y), find the partial derivatives fu, fa, and fy.

25 = d. Assuming f(w, x,y) (6w+1) cos(3x² + 4xy³ + y), find the partial derivatives fu, fa, and fy.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 20E
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Please help with just D, please
a. If f(x, y) = 3x³ - 2x2y5, find the partial derivatives fz and fy. +₁=2 Əx -(2x³ - 2x²y4) = 9x² - 4x4 fy=2(3x³-2x2y4) = -8x2y3 find the partial derivatives fr and fy. b. If f(x, y) = ry² x+1' fx Fx = 2 (x4² ) = (x+1) y ² - xy² = 24/1/2 = (x + 1/² 2 =42 (x+1)2 (X+1) (x+1² xy=-3 (2-) = 2x4 c. If g(r, s) = rs cos(r), find the partial derivatives g, and g.. g(₁,5) = rscos(r) g₁= = (cos(r)) = S(os(c)-rssin (r) dr. gs=d& (rescos (r)) = rcsos (r) d. Assuming f(w, x, y) = (6w+1) cos(3x² + 4xy³ + y), find the partial derivatives fw, fa, and fy. x2z³ 1+1² e. Find all possible first-order partial derivatives of g(x, t, z) = 9-=-2 (x² + 3³²) = x² + 2²-1-(23) x2+z3 2+ 9x=2+₂ ³ 1+23 2 + 2₂2 = 3x² ¹/2 ² 1+23 -3_x³² 2 5 [1+2³]²
Transcribed Image Text:a. If f(x, y) = 3x³ - 2x2y5, find the partial derivatives fz and fy. +₁=2 Əx -(2x³ - 2x²y4) = 9x² - 4x4 fy=2(3x³-2x2y4) = -8x2y3 find the partial derivatives fr and fy. b. If f(x, y) = ry² x+1' fx Fx = 2 (x4² ) = (x+1) y ² - xy² = 24/1/2 = (x + 1/² 2 =42 (x+1)2 (X+1) (x+1² xy=-3 (2-) = 2x4 c. If g(r, s) = rs cos(r), find the partial derivatives g, and g.. g(₁,5) = rscos(r) g₁= = (cos(r)) = S(os(c)-rssin (r) dr. gs=d& (rescos (r)) = rcsos (r) d. Assuming f(w, x, y) = (6w+1) cos(3x² + 4xy³ + y), find the partial derivatives fw, fa, and fy. x2z³ 1+1² e. Find all possible first-order partial derivatives of g(x, t, z) = 9-=-2 (x² + 3³²) = x² + 2²-1-(23) x2+z3 2+ 9x=2+₂ ³ 1+23 2 + 2₂2 = 3x² ¹/2 ² 1+23 -3_x³² 2 5 [1+2³]²
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