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Find the second-order partial derivative. 19) Let H(x, y) = (3xy/x^2 - y). Find

Question : Find the second-order partial derivative. 19) Let H(x, y) = (3xy/x^2 - y). Find : 2163353

Find the second-order partial derivative.

19) Let H(x, y) = (3xy/x2 - y). Find (∂2H/∂y2).

A) (9x4 - 6x3 - 9x2y/(x2 - y)3)

B) (3x3/(x2 - y)2)

C) (6x3/(x2 - y)3)

D) (6x3y - 6x5/(x2 - y)4)

E) none of these

20) Let F(x, y, z) = (xz/y2z + x) - 5x2y3. Compute (∂F/∂y)(-1, 0, 1).

A) - (1/2)

B) 2

C) (3/5)

D) 0

E) none of these

21) Let P(x, y, z) = xy + 2x3√(y2 - 1). Compute (∂P/∂z)(2, 1, 3).

A) 1

B) 3

C) 2

D) 0

E) none of these

22) Let f(x, y) = x3y + ex + 3y. Compute (∂2f/∂x ∂y)(1, 0).

A) 3 + e

B) 3 + 3e

C) 6 + e

D) 6

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

23) Let f(x, y) = (x2 + x)ey - x. Find (∂f/∂x).

Enter your answer as just (P(x))ey - x where P is a polynomial in x in standard form.

24) Let f(x, y) = 4y2 - 2x3 + 5xy2. Find (∂f/∂x).

Enter just a polynomial in x plus or minus a polynomial in y both in standard form (do not label, no parentheses).

25) Let f(x, y) = ex^2y. Find (∂f/∂y).

Enter your answer exactly as just ex^2y(P(x)) where P is a polynomial in x in standard form (do not label).

26) Let f(x, y) = x2 + y. Find (∂f/∂y).

Enter just an integer.

27) Let f(x, y) = 3x2 + 2xy. Find (∂f/∂x).

Enter your answer exactly as just a polynomial in x plus or minus a polynomial in y both in standard form (do not label, no parentheses).

28) Let f(x, y) = x2 + 2xy + ey. Find (∂f/∂y).

Enter just a polynomial in x plus or minus a polynomial in ey both in standard form (do not label, no parentheses).

29) Let f(x, y) = 4x2 + 2y2/3 + ex^4/3. Find (∂f/∂y).

Enter just a power function in y in standard form (do not label).

30) Let f(x, y) = 4x2 + 2y2 + 3xy. Find (∂f/∂y).

Enter just a polynomial in y plus or minus a polynomial in x both in standard form (no label, no parentheses).

31) Let f(x, y) = 2y3 + 4x4 + 2xy. Find (∂f/∂y).

Enter just a polynomial in y plus or minus a polynomial in x both in standard form (no label, no parentheses).

32) Let f(x, y, z) = ln(xy2z3). Find (∂f/∂z).

Enter your answer in the unlabeled form azb.

33) Let f(x, y) = x2y + y2x + 2xy. Find (∂2f/∂x ∂y).

Enter just a polynomial in x plus or minus a polynomial in y plus or minus two, both polynomials in standard form (no label, no parentheses).

34) Let f(x, y) = (x/y + 1). Find (∂2f/∂x ∂y).

Enter just ±(P(y))a where P is a polynomial in standard form (do not label).

35) Let f(x, y) = y(x + ey - x). Compute (∂f/∂x)(2, 3).

Enter your answer exactly as just a(b ± E).

36) Let f(x, y) = xy. Find (∂f/∂x) and (∂f/∂y). Is y, x correct in the corresponding order?

Enter "yes" or "no".

37) Let f(x, y) = x2y - xy2. Find (∂f/∂x). Is y2 + 2xy the correct answer?

Enter "yes" or "no".

Solution
5 (1 Ratings )

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Calculus 2 Months Ago 48 Views
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