Find the derivative of: f ( x ) = 4 x f\left(x\right)=4\sqrt{x} f ( x ) = 4 x <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">

f ′ ( x ) = 2 x f'\left(x\right)=\frac{2}{\sqrt{x}} f ′ ( x ) = x <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"> 2

f ′ ( x ) = 2 x f'\left(x\right)=2\sqrt{x} f ′ ( x ) = 2 x <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">

f ′ ( x ) = 4 x 1 2 f'\left(x\right)=4x^{\frac{1}{2}} f ′ ( x ) = 4 x 2 1

f ′ ( x ) = 2 x − 1 2 f'\left(x\right)=2x^{-\frac{1}{2}} f ′ ( x ) = 2 x − 2 1

Find the derivative: f ( x ) = x 12 5 + 3 x 7 5 f\left(x\right)=x^{\frac{12}{5}}+3x^{\frac{7}{5}} f ( x ) = x 5 1 2 + 3 x 5 7

f ′ ( x ) = x 7 5 + 3 x 2 5 f'\left(x\right)=x^{\frac{7}{5}}+3x^{\frac{2}{5}} f ′ ( x ) = x 5 7 + 3 x 5 2

f ′ ( x ) = 12 x 7 5 + 21 x 2 5 f'\left(x\right)=12x^{\frac{7}{5}}+21x^{\frac{2}{5}} f ′ ( x ) = 1 2 x 5 7 + 2 1 x 5 2

Find the derivative f(x) = x 2 /e x

f'(x) = (2xe x - x 2 e x ) / (e x ) 2

f'(x) = (x 2 e x - 2xe x ) / (e x ) 2

f'(x) = (2xe x + x 2 e x ) / (e x ) 2

Which expression would find the instant rate of change for sin2x at x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

lim ⁡ x → 5 π 3 sin ⁡ 2 x + 3 2 x − 5 π 3 \lim_{x\rightarrow\ \frac{5\pi}{3}}\ \frac{\sin2x+\frac{\sqrt{3}}{2}}{x-\frac{5\pi}{3}} x → 3 5 π lim x − 3 5 π sin 2 x + 2 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

10 π 3 \frac{10\pi}{3} 3 1 0 π

Derivative Rules

Authored by John Getz

Mathematics

11th - 12th Grade

CCSS covered

Used 37+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative of:
$f\left(x\right)=\frac{2}{x^2}-\frac{9}{x}$

$f'\left(x\right)=-\frac{4}{x^3}+\frac{9}{x^2}$

$f'\left(x\right)=-\frac{4}{x}+9$

$f'\left(x\right)=\frac{2}{x^3}-\frac{9}{x^2}$

$f'\left(x\right)=\frac{4}{x^3}-\frac{9}{x^2}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative of:
$f\left(x\right)=x^9-7x^5+3x+13$

$f'\left(x\right)=9x^8-35x^4+3$

$f'\left(x\right)=x^8-7x^4+3$

$f'\left(x\right)=9x^9-35x^5+3x$

$f'\left(x\right)=9x^8-35x^4+3+13$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative of:
$f\left(x\right)=4\sqrt{x}$

$f'\left(x\right)=\frac{2}{\sqrt{x}}$

$f'\left(x\right)=2\sqrt{x}$

$f'\left(x\right)=4x^{\frac{1}{2}}$

$f'\left(x\right)=2x^{-\frac{1}{2}}$

Tags

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative:
$f\left(x\right)=x^{\frac{12}{5}}+3x^{\frac{7}{5}}$

$f'\left(x\right)=\frac{12}{5}x^{\frac{7}{5}}+\frac{21}{5}x^{\frac{2}{5}}$

$f'\left(x\right)=x^{\frac{7}{5}}+3x^{\frac{2}{5}}$

$f'\left(x\right)=12x^{\frac{7}{5}}+21x^{\frac{2}{5}}$

$f'\left(x\right)=\frac{12}{5}x^{\frac{4}{5}}+\frac{21}{5}x^{\frac{1}{5}}$

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the derivative:
y=4e^x²

y'=8xe^x

y'=8xe^x²

y'=8xe^2x

y'=8xe^4x²

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative:
y=(2^3x+4)

3(ln2)(2^3x+4)

3(2^3x+4)

3(2^3x+4/(ln2))

2^3x+4

Tags

CCSS.HSF.BF.B.5

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Derivative Rules

Find the derivative of:
$f\left(x\right)=\frac{2}{x^2}-\frac{9}{x}$

Find the derivative of:
$f\left(x\right)=x^9-7x^5+3x+13$

Find the derivative of:
$f\left(x\right)=4\sqrt{x}$

Find the derivative:
$f\left(x\right)=x^{\frac{12}{5}}+3x^{\frac{7}{5}}$

Find the derivative:
y=4e^x²

Find the derivative:
y=(2^3x+4)

Find the derivative:
y=e^5x+ln(x)

Find the derivative:
y = 3ln(x²-3)

Find the derivative:
y=5x²e^3x

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Popular Resources on Wayground

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Derivative Rules

Find the derivative of: f(x)=2x2−9xf\left(x\right)=\frac{2}{x^2}-\frac{9}{x}f(x)=x22​−x9​

Find the derivative of: f(x)=x9−7x5+3x+13f\left(x\right)=x^9-7x^5+3x+13f(x)=x9−7x5+3x+13

Find the derivative of: f(x)=4xf\left(x\right)=4\sqrt{x}f(x)=4x​

Find the derivative: f(x)=x125+3x75f\left(x\right)=x^{\frac{12}{5}}+3x^{\frac{7}{5}}f(x)=x512​+3x57​

Find the derivative:y=4ex²

Find the derivative:y=(23x+4)

Find the derivative:y=e5x+ln(x)

Find the derivative:y = 3ln(x2-3)

Find the derivative:y=5x2e3x

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the derivative of:
$f\left(x\right)=\frac{2}{x^2}-\frac{9}{x}$

Find the derivative of:
$f\left(x\right)=x^9-7x^5+3x+13$

Find the derivative of:
$f\left(x\right)=4\sqrt{x}$

Find the derivative:
$f\left(x\right)=x^{\frac{12}{5}}+3x^{\frac{7}{5}}$

Find the derivative:
y=4e^x²

Find the derivative:
y=(2^3x+4)

Find the derivative:
y=e^5x+ln(x)

Find the derivative:
y = 3ln(x²-3)

Find the derivative:
y=5x²e^3x