Chain Rule Theorem and Review

Authored by Greg Snelick

Mathematics

9th Grade

Used 3+ times

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10 questions

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DRAG AND DROP QUESTION

1 min • 2 pts

CHAIN RULE THEOREM
$u=g\left(x\right)$
(a) is a differentiable function of (b)
DERIVATIVE NOTATIONS
$u'=g'\left(x\right)=$ (c) $=$ (d) $=$ (e)

$u$

$x$

$\frac{du}{dx}$

$\frac{d}{dx}\left[g\left(x\right)\right]$

$D_{\ x}\ u$

\frac{dx}{du}

D_{\ u}\ x

g

\frac{dg}{dx}

DRAG AND DROP QUESTION

1 min • 2 pts

CHAIN RULE THEOREM
$y=h\left(u\right)$
(a) is a differentiable function of (b)
DERIVATIVE NOTATIONS
$y'=h'\left(u\right)=$ (c) $=$ (d) $=$ (e)

$y$

$u$

$\frac{dy}{du}$

$\frac{d}{du}\left[h\left(u\right)\right]$

$D_{\ u}\ y$

\frac{du}{dy}

D_{\ y}\ u

h

\frac{dh}{du}

DROPDOWN QUESTION

1 min • 2 pts

CHAIN RULE THEOREM
$u=$ (a) and $y=$ (b)
(using substitution)
$y=$ (c) ( (d) ( (e) ) )

$g\left(x\right)$

$h\left(u\right)$

$h$

$g$

$x$

g\left(u\right)

h\left(x\right)

u

FILL IN THE BLANKS QUESTION

1 min • 2 pts

CHAIN RULE THEOREM
$y=h\left(g\left(x\right)\right)$
$y$ is a WORD function
Submit WORD (small letters)

(a)

DRAG AND DROP QUESTION

1 min • 2 pts

CHAIN RULE (Parts Identification)
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
$\frac{dy}{dx}=$ (a) $\cdot$ (b)

$\frac{dy}{du}$

$\frac{du}{dx}$

\frac{du}{dy}

\frac{dx}{du}

\frac{dg}{dh}

\frac{dh}{dg}

DRAG AND DROP QUESTION

1 min • 2 pts

ALTERNATE CHAIN RULE
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
(a) $\left[h\left(g\left(x\right)\right)\right]=$ (b) $\cdot$ (c)

$\frac{d}{dx}$

$h'\left(g\left(x\right)\right)$

$g'\left(x\right)$

\frac{d}{du}

h'\left(u\right)

\frac{d}{dh}

MATH RESPONSE QUESTION

1 min • 2 pts

CHAIN RULE REVIEW
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
FUNCTION
$y=24\left(13x^{18}+5\right)^{34}$
$u=EXP\ 1\ \ and\ y=EXP\ 2$
$\frac{du}{dx}=EXP\ 3\ \ and\ \ \frac{dy}{du}=EXP\ 4$
Submit $EXP\ 1$

$13x^{18}+5$

Mathematical Equivalence

MATH RESPONSE QUESTION

1 min • 2 pts

CHAIN RULE REVIEW
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
FUNCTION
$y=24\left(13x^{18}+5\right)^{34}$
$u=EXP\ 1\ \ and\ y=EXP\ 2$
$\frac{du}{dx}=EXP\ 3\ \ and\ \ \frac{dy}{du}=EXP\ 4$
Submit $EXP\ 2$

$24u^{34}$

Mathematical Equivalence

OFF

MATH RESPONSE QUESTION

1 min • 2 pts

CHAIN RULE REVIEW
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
FUNCTION
$y=24\left(13x^{18}+5\right)^{34}$
$u=EXP\ 1\ \ and\ y=EXP\ 2$
$\frac{du}{dx}=EXP\ 3\ \ and\ \ \frac{dy}{du}=EXP\ 4$
Submit $EXP\ 3$

$234x^{17}$

Mathematical Equivalence

OFF

10.

MATH RESPONSE QUESTION

1 min • 2 pts

CHAIN RULE REVIEW
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
FUNCTION
$y=24\left(13x^{18}+5\right)^{34}$
$u=EXP\ 1\ \ and\ y=EXP\ 2$
$\frac{du}{dx}=EXP\ 3\ \ and\ \ \frac{dy}{du}=EXP\ 4$
Submit $EXP\ 4$

$816u^{33}$

Mathematical Equivalence

OFF

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Chain Rule Theorem and Review

CHAIN RULE THEOREM u=g(x)u=g\left(x\right)u=g(x) ​ (a) is a​ differentiable function of​ (b) DERIVATIVE NOTATIONS ​ ​ u′=g′(x)=u'=g'\left(x\right)=u′=g′(x)= ​ (c) === ​ (d) === ​ (e)

CHAIN RULE THEOREM y=h(u)y=h\left(u\right)y=h(u) ​ (a) is a​ differentiable function of​ (b) DERIVATIVE NOTATIONS ​ ​ y′=h′(u)=y'=h'\left(u\right)=y′=h′(u)= ​ (c) === ​ (d) === ​ (e)

​ CHAIN RULE THEOREM u=u=u= ​ (a) and y=y=y= ​ (b) (using substitution) y=y=y= ​ (c) (​ (d) (​ (e) ) )

CHAIN RULE THEOREM y=h(g(x))y=h\left(g\left(x\right)\right)y=h(g(x)) yyy is a WORD functionSubmit WORD (small letters) (a)

CHAIN RULE (Parts Identification) u=g(x) and y=h(u)u=g\left(x\right)\ \ and\ \ y=h\left(u\right)u=g(x) and y=h(u) dydx=\frac{dy}{dx}=dxdy​= ​ (a) ⋅\cdot⋅ ​ (b)

ALTERNATE CHAIN RULE u=g(x) and y=h(u)u=g\left(x\right)\ \ and\ \ y=h\left(u\right)u=g(x) and y=h(u) ​ (a) [h(g(x))]=\left[h\left(g\left(x\right)\right)\right]=[h(g(x))]= ​ (b) ⋅\cdot⋅ ​ (c)

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CHAIN RULE THEOREM
$u=g\left(x\right)$
(a) is a differentiable function of (b)
DERIVATIVE NOTATIONS
$u'=g'\left(x\right)=$ (c) $=$ (d) $=$ (e)

CHAIN RULE THEOREM
$y=h\left(u\right)$
(a) is a differentiable function of (b)
DERIVATIVE NOTATIONS
$y'=h'\left(u\right)=$ (c) $=$ (d) $=$ (e)

CHAIN RULE THEOREM
$u=$ (a) and $y=$ (b)
(using substitution)
$y=$ (c) ( (d) ( (e) ) )

CHAIN RULE THEOREM
$y=h\left(g\left(x\right)\right)$
$y$ is a WORD function
Submit WORD (small letters)

(a)

CHAIN RULE (Parts Identification)
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
$\frac{dy}{dx}=$ (a) $\cdot$ (b)

ALTERNATE CHAIN RULE
$u=g\left(x\right)\ \ and\ \ y=h\left(u\right)$
(a) $\left[h\left(g\left(x\right)\right)\right]=$ (b) $\cdot$ (c)