← Partial Derivatives & Chain Rule

Practice: Partials & Chain Rule

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

If

f (x, y) = x^{3} y^{2} + 5 y

, then

f_{x}

equals

Q2.

intermediateFinal Review #48

If

f (x, y, z) = e^{x z} sin (y / z)

, then

f_{y}

equals

Q3.

basic

If

f

has continuous second partials, then

Q4.

intermediate

If

z = x^{2} y

where

x = cos t, y = sin t

, then

d z / d t

equals

Q5.

advanced

f_{x y}

for

f (x, y) = x^{2} e^{x y}

equals

Q6.

intermediateFinal Review #53

If

z

is defined implicitly by

x^{2} + y^{2} + z^{2} = 1

, then

\partial z / \partial x

equals (assuming

z \neq = 0

)

Q7.

intermediate

Suppose

z = f (s, t)

where

s = x + y, t = x y

. Then

\partial z / \partial x

equals

Q8.

intermediate

Compute

\partial^{2} f / \partial x^{2}

at

(0, 0)

if

f (x, y) = cos (x + y^{2})

.