Q. 5 Fill in the blanks to complete e... [FREE SOLUTION]

Chapter 12: Q. 5 (page 988)

Fill in the blanks to complete each of the following theorem statements:
The chain rule: Given functions $z = f (x, y)$ , $x = u (s, t)$ , and $y = v (s, t)$ , for all values of $s$ and $t$ at which $u$ and $v$ are differentiable, and if $f$ is differentiable at $(u (s, t), v (s, t))$ , then $\frac{鈭� z}{鈭� s} =_$ and $\frac{鈭� z}{鈭� t} =_$ .

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The chain rule: Given functions $z = f (x, y)$ , $x = u (s, t)$ , and $y = v (s, t)$ , for all values of $s$ and $t$ at which $u$ and $v$ are differentiable, and if $f$ is differentiable at $(u (s, t), v (s, t))$ , thenrole="math" localid="1654181399600" $\frac{鈭� z}{鈭� s} = \frac{鈭� z}{鈭� x} \frac{鈭� x}{鈭� s} + \frac{鈭� z}{鈭� y} \frac{鈭� y}{鈭� s}$ and $\frac{鈭� z}{鈭� t} = \frac{鈭� z}{鈭� x} \frac{鈭� x}{鈭� t} + \frac{鈭� z}{鈭� y} \frac{鈭� y}{鈭� t}$ .

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The chain rule: Given functions $z = f (x, y)$ , $x = u (s, t)$ , and $y = v (s, t)$ , for all values of $s$ and $t$ at which $u$ and $v$ are differentiable, and if $f$ is differentiable at $(u (s, t), v (s, t))$ , then $\frac{鈭� z}{鈭� s} = \frac{鈭� z}{鈭� x} \frac{鈭� x}{鈭� s} + \frac{鈭� z}{鈭� y} \frac{鈭� y}{鈭� s}$ and $\frac{鈭� z}{鈭� t} = \frac{鈭� z}{鈭� x} \frac{鈭� x}{鈭� t} + \frac{鈭� z}{鈭� y} \frac{鈭� y}{鈭� t}$ .

This is the chain rule adapted for the function of two variables.

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Fill in the blanks to complete each of the following theorem statements:The chain rule: Given functions z=f(x,y), x=u(s,t), and y=v(s,t), for all values of sand tat which uand vare differentiable, and if fis differentiable at (u(s,t),v(s,t)), then鈭�z鈭�s=_____and鈭�z鈭�t=_____.

Short Answer

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Step 2. Filling in the blanks

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Recommended explanations on Math Textbooks

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Calculus

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Decision Maths

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