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- Calculus 3
- Partial Derivatives

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Get Started Now- Intro Lesson: a1:07
- Intro Lesson: b5:05
- Intro Lesson: c5:02
- Lesson: 15:17
- Lesson: 23:54
- Lesson: 37:12
- Lesson: 47:26

Suppose there is a 2-variable function $z=f(x,y)$. Then we say that the differential $dz$ is:

$dz = f_xdx + f_ydy$

Of course, differentials can be extended to 3-variable functions as well. Suppose there is a 3-variable function $w=g(x,y, z)$. Then we say that the differential $dw$ is:

$dw = g_x dx + g_y dy + g_z dz$

- Introduction
**Differentials of Multivariable Functions Overview:**a)__A Review of Differentials__- $dy, dx$ are differentials
- $dy=f'(x)dx$

b)__Differentials of 2 Variable Functions__- Differential $dz$
- $dz=f_xdx+f_ydy$
- An example

c)__Differentials of 3 Variable Functions__- Differential $dw$
- $dw=g_xdx+g_ydy+g_zdz$
- An example

- 1.
**Finding Differentials of 2 Variable Functions**

Compute the differential for the following function:$f(x,y) = e^{x^3+y^3} \sin \frac{x}{2}$

- 2.Compute the differential for the following function:
$z = ln (\frac{x^2 y^3 }{2} )$

- 3.
**Finding Differentials of 3 Variable Functions**Compute the differentials for the following function:$g(x,y,z) = \tan [ \ln (xy^2 z^3) ]$

- 4.Compute the differentials for the following function:
$g = \frac{e^{xy}}{xy^2z^2}$