d y d x i f y = e ( 7 − 9 x ) \frac{dy}{dx}\ if\ y=e^{\left(7-9x\right)} d x d y i f y = e ( 7 − 9 x ) Find

− 9 e ( 7 − 9 x ) -9e^{\left(7-9x\right)} − 9 e ( 7 − 9 x )

− 9 ln ⁡ ( 7 − 9 x ) -9\ln\left(7-9x\right) − 9 ln ( 7 − 9 x )

7 e ( 7 − 9 x ) 7e^{\left(7-9x\right)} 7 e ( 7 − 9 x )

d y d x i f y = ln ⁡ 2 x \frac{dy}{dx}if\ y=\ln2x d x d y i f y = ln 2 x Find

− 1 2 x \frac{-1}{2x} 2 x − 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 )

Basic Chain Rule

Quiz

•

Mathematics

•

11th Grade - University

•

Practice Problem

•

Hard

•

CCSS

HSF.IF.A.2, HSF-IF.C.8B, HSA.APR.A.1

+7

Standards-aligned

Elizabeth Bushek

FREE Resource

18 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the derivative of $y=\left(8x-3\right)^6$

$48\left(8x-3\right)^5$

$-48\left(8x-3\right)^5$

$14\left(8x-3\right)^5$

$-14\left(8x-3\right)^5$

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the derivative of $y=\left(2x-1\right)^3$

$6\left(2x-1\right)^2$

$3\left(2x-1\right)^2$

$-3\left(2x-1\right)^2$

$-4\left(2x-1\right)^2$

3.

MULTIPLE CHOICE QUESTION

15 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

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

find y' for y= sin(2x²)

4sin(2x²)

4xcos(2x²)

2xcos(2x²)

xcos(4x²)

5.

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

Find dy/dx if y = cos⁵x

5cos⁴x

-5sin⁴x

5cos⁴xsinx

-5cos⁴xsinx

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find y' if y = tan(3x²+2).

sec²(3x²+2)

6xsec²(3x²+2)

6xsec²x(3x²+2)

sec²(6x)

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