16. f(x, y) = x+y³ + 8x²y

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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16) Find the first partial derivatives of the function.

f(x, y) = x^4y^3 + 8x^2 y

15-38 Find the first partial derivatives of the function.
15. f(x, y) = y5 - 3xy
17. f(x, t) = e 'cos TX
19. z = (2x + 3y) ¹⁰
x-y
21. f(x, y)
=
x + y
23. w = sin a cos B
25. f(r, s) = r ln(r² + s²)
27. u = te¹0/t
29. f(x, y, z) = xz - 5x²y³z4
31. w = - In(x + 2y + 3z)
33. u = xy sin ¹(yz)
35. f(x, y, z, t) = xyz² tan(yt)
37. u =
√x² + x² +
+ x/²/2/2
38. u =
sin(x₁ + 2x₂ +
16. f(x, y) = x+y³ + 8x²y
18. f(x, t) = √√√x In t
20. z = tan xy
22. f(x, y) = x²
24. w = e/(u + v²)
26. f(x, t)
=
arctan (x√√7)
28. f(x, y) = f*cos(1²) dt
30. f(x, y, z) = x sin(y - z)
32. w = ze.xyz
34. u=
=xy/z
xy²
36. f(x, y, z, t)
t + 2z
+ nxn)
Transcribed Image Text:15-38 Find the first partial derivatives of the function. 15. f(x, y) = y5 - 3xy 17. f(x, t) = e 'cos TX 19. z = (2x + 3y) ¹⁰ x-y 21. f(x, y) = x + y 23. w = sin a cos B 25. f(r, s) = r ln(r² + s²) 27. u = te¹0/t 29. f(x, y, z) = xz - 5x²y³z4 31. w = - In(x + 2y + 3z) 33. u = xy sin ¹(yz) 35. f(x, y, z, t) = xyz² tan(yt) 37. u = √x² + x² + + x/²/2/2 38. u = sin(x₁ + 2x₂ + 16. f(x, y) = x+y³ + 8x²y 18. f(x, t) = √√√x In t 20. z = tan xy 22. f(x, y) = x² 24. w = e/(u + v²) 26. f(x, t) = arctan (x√√7) 28. f(x, y) = f*cos(1²) dt 30. f(x, y, z) = x sin(y - z) 32. w = ze.xyz 34. u= =xy/z xy² 36. f(x, y, z, t) t + 2z + nxn)
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