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Find the partial derivative. 1) f(x, y) = 10x - 10y^2 - 4. Find

Question : Find the partial derivative. 1) f(x, y) = 10x - 10y^2 - 4. Find : 2163350

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the partial derivative.

1) f(x, y) = 10x - 10y2 - 4. Find (∂f/∂x).

A) 6

B) 10

C) 10x

D) -20y

2) f(x,y) = 3x2 - 15xy + 7y3. Find (∂f/∂x).

A) -15x + 21y2

B) 6x2 - 15x

C) 6x - 15y

D) 6x - 15y + 21y2

3) f(x, y) = (x + y)5. Find (∂f/∂x).

A) 5(x + y)

B) 5y(x + y)4

C) 5x(x + y)4

D) 5(x + y)4

4) f(x, y) = 3(x + 7y - 5)2. Find (∂f/∂y).

A) 21x + 147y

B) 42x + 294y - 210

C) 42x + 294y + 210

D) 21x + 147y - 105

5) f(x, y) = e-2x + 3y. Find (∂f/∂x).

A) fx(x, y) = -2e-2x

B) fx(x, y) = 3e-2x + 3y

C) fx(x, y) = e-2x + 3

D) fx(x, y) = -2e-2x + 3y

6) f(x, y) = e2xy. Find (∂f/∂x).

A) fx(x, y) = 2ye2xy

B) fx(x, y) = 2(x + y)e2xy

C) fx(x, y) = 2e2xy

D) fx(x, y) = 2ye2x

7) f(x, y) = xln(9x + 4y). Find (∂f/∂x).

A) fx(x, y) = ln(9x + 4y)

B) fx(x, y) = (9x/9x + 4y)

C) fx(x, y) = ln(9x + 4y) + (9/9x + 4y)

D) fx(x, y) = (9x/9x + 4y) +ln(9x + 4y)

8) f(x, y) = (2x/y) - (y/2x). Find (∂f/∂x).

A) fx(x, y) = (2x2/y) + (y/2x2)

B) fx(x, y) = (2/y) + (y/2x2)

C) fx(x, y) = - (2/y2) - (2/y)

D) fx(x, y) = (2/y) - (y/2x2)

9) Find (∂f/∂x)(3, -5) when f(x,y) = 7x2 - 9xy.

A) -3

B) 3

C) -72

D) 87

10) Find (∂f/∂y)(2, -3) when f(x, y) = 7xy - 6y.

A) 14

B) 0

C) -21

D) 8

11) Find (∂f/∂x)(-4, 5) when f(x, y) = (2x + 5y)2.

A) -32

B) 68

C) 34

D) 14

12) Find (∂f/∂x) for f(x, y, z) = 2x8y3 + 6x3z5 + 7y10.

A) 6x8y2 + 30x3z4

B) 16x7 + 18x2

C) 48x7y2 + 90x2z4

D) 16x7y3 + 18x2z5

Find the second-order partial derivative.

13) Find (∂2f/∂x2), where f(x, y) = x4y5 + x5y.

A) 4x3y5 + 5x4y

B) 20y3

C) 12x2y5 + 20x3y

D) 12x2y5 + 20x3

14) Let f(x, y) = (1/2)x2⋅ex/y. Find (∂f/∂y).

A) - (x3/2y2)ex/y

B) (x2/y)ex/y

C) (x3/y)ex/y - 1

D) (1/2)x2ex/y

E) none of these

15) Let f(x, y, z) = xyz(1 + eyz). Find (∂f/∂z).

A) xy(1 + eyz) + xy(1 + yeyz)

B) xy(1 + ey)

C) xy(1 + eyz) + xy2zeyz

D) xy(1 + yeyz)

E) none of these

16) Let G(x, r, t) = 2x2t + (1/3)t2 - r3√(xt). Find (∂G/∂x).

A) 4xt + (1/3)t2 - r3(1/2√(xt))

B) 4x - (r3/2√(xt))

C) 4xt - (1/3)t2 - (3r2t/2√(xt))

D) 4xt - (r3t/2√(xt))

E) none of these

17) Let f(x, y, z) = y3z - x2y + √(xyz) - (1/x). Find (∂f/∂y).

A) 3y2 - 2x + 1

B) 3y2z - x2 + (xz/2√(xyz))

C) 3y2z - x2 + (xz/√(xyz)) + (1/x2)

D) 3y2z - x2 + √(xz)

E) none of these

18) Let g(x, t, z) = (1/t)(x - z2t). Find (∂2g/∂z ∂t).

A) - (2z/t) + 1

B) -2zt + t2

C) -2zt

D) 0

E) none of these

Solution
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