Find d p d q i f p = 1 q + 9 \frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}} d q d p i f p = q + 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1

− 1 2 ( q + 9 ) 3 2 -\frac{1}{2\left(q+9\right)^{\frac{3}{2}}} − 2 ( q + 9 ) 2 3 1

1 2 ( q + 9 ) 3 2 \frac{1}{2\left(q+9\right)^{\frac{3}{2}}} 2 ( q + 9 ) 2 3 1

− 1 ( q + 9 ) 3 2 -\frac{1}{\left(q+9\right)^{\frac{3}{2}}} − ( q + 9 ) 2 3 1

− 1 q + 9 -\frac{1}{\sqrt{q+9}} − q + 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1

d y d t i f y = cos ⁡ 10 t + 12 \frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12} d t d y i f y = cos 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> Find

− 5 10 t + 12 sin ⁡ 10 t + 12 \frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12} 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 5 sin 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 1 2 10 t + 12 sin ⁡ 10 t + 12 \frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12} 2 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1 sin 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− sin ⁡ 10 t + 12 -\sin\sqrt{10t+12} − sin 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− sin ⁡ ( 5 10 t + 12 ) -\sin\left(\frac{5}{\sqrt{10t+12}}\right) − sin ( 1 0 t + 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 5 )

Chain rule

Authored by Nadira Herenda

Mathematics

11th Grade - Professional Development

CCSS covered

Used 29+ times

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10 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the derivative of f(x) = (x⁶ + 4)⁵

f '(x) = 5x⁵(x⁴ + 4)⁴

f '(x) = 6x⁵(x⁶ + 4)⁴

f '(x) = 30x⁵(x⁶ + 4)⁴

f '(x) = 30x⁶(x⁶ + 4)⁴

MULTIPLE CHOICE QUESTION

3 mins • 12 pts

Find the derivative of f(x)=(x³-2x)²

6x⁵ - 12x³+8x

6x⁵ - 16x³+8x

x⁶-4x⁴+4x²

6x⁵ - 16x^3-8x

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

3 mins • 12 pts

Tags

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

find y' for y=(e^5x)+1

5e^5x+1

e^5x

5e^5x

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

find y' for y= sin(2x²)

4sin(2x²)

4xcos(2x²)

2xcos(2x²)

xcos(4x²)

MULTIPLE CHOICE QUESTION

3 mins • 12 pts

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.1

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the derivative.
f(z) = 1/(3z²) + 4z³

f'(z) = 6z³ + 12z²

f'(z) = 6z + 12x²

f'(z) = -2/(3z³) + 12z²

f'(z) = -6/z² + 12z²

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find $\frac{dv}{dt}\ if\ v=t+\frac{8}{t}$

$1-\frac{8}{t^2}$

$1-\frac{8}{t}$

$t-\frac{8}{t^2}$

$1+\frac{8}{t^2}$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find $\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}$

$-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$

$\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$

$-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}$

$-\frac{1}{\sqrt{q+9}}$

Tags

CCSS.HSN.RN.A.2

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}$ Find

$\frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12}$

$\frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12}$

$-\sin\sqrt{10t+12}$

$-\sin\left(\frac{5}{\sqrt{10t+12}}\right)$

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Chain rule

Find the derivative of f(x) = (x6 + 4)5

Find the derivative of f(x)=(x3-2x)2

find y' for y=(e5x)+1

find y' for y= sin(2x2)

Find the derivative. f(z) = 1/(3z2) + 4z3

Find dvdt if v=t+8t\frac{dv}{dt}\ if\ v=t+\frac{8}{t}dtdv​ if v=t+t8​

Find dpdq if p=1q+9\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}dqdp​ if p=q+9​1​

dydt if y=cos⁡10t+12\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}dtdy​ if y=cos10t+12​ Find

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Find the derivative of f(x) = (x⁶ + 4)⁵

Find the derivative of f(x)=(x³-2x)²

find y' for y=(e^5x)+1

find y' for y= sin(2x²)

Find the derivative.
f(z) = 1/(3z²) + 4z³

Find $\frac{dv}{dt}\ if\ v=t+\frac{8}{t}$

Find $\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}$

$\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}$ Find