The General Power Rule says that d d x [ x n ] = \frac{d}{dx}\left[x^n\right]= d x d [ x n ] =

n x n − 1 nx^{n-1} n x n − 1

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

How can you change this to power form: 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 ) = 4 x 1 2 f\left(x\right)=4x^{\frac{1}{2}} f ( x ) = 4 x 2 1

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

Derivative Rules

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CCSS

HSA.SSE.B.3, HSF.IF.A.2, HSA.APR.D.7

Standards-aligned

Adam Hosler

Used 141+ times

FREE Resource

10 questions

Show all answers

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

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The General Power Rule says that
$\frac{d}{dx}\left[x^n\right]=$

$nx^{n-1}$

$x^{n-1}$

$nx^n$

$x^n$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

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

Find the derivative of:
$f\left(x\right)=\frac{3}{4}x-8$

$\frac{3}{4}$

$-8$

Find the derivative:
$f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$

$f'\left(t\right)=-\frac{1}{t^2}+\frac{6}{t^3}-\frac{15}{t^4}$

$f'\left(t\right)=-t^{-2}+6t^{-3}-15t^{-4}$

$f'\left(t\right)=t^{-1}-3t^{-2}+5t^{-3}$

$f'\left(t\right)=\frac{1}{t^2}+\frac{6}{t^3}-\frac{15}{t^4}$

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

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

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

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

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

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Derivative Rules

10 questions

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

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

The General Power Rule says that
$\frac{d}{dx}\left[x^n\right]=$

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

Find the derivative of:
$f\left(x\right)=\frac{3}{4}x-8$

Find the derivative:
$f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$

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

How do you rewrite this in power form:
$f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$

How can you change this to power form:
$f\left(x\right)=4\sqrt{x}$

Find the derivative of:
$f\left(x\right)=3x^7-6x^6-10x^4+3x^3-15x-21$

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Derivative Rules

10 questions

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

The General Power Rule says that ddx[xn]=\frac{d}{dx}\left[x^n\right]=dxd​[xn]=

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

Find the derivative of: f(x)=34x−8f\left(x\right)=\frac{3}{4}x-8f(x)=43​x−8

Find the derivative: f(t)=1t−3t2+5t3f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}f(t)=t1​−t23​+t35​

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

How do you rewrite this in power form: f(t)=1t−3t2+5t3f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}f(t)=t1​−t23​+t35​

How can you change this to power form: f(x)=4xf\left(x\right)=4\sqrt{x}f(x)=4x​

Find the derivative of: f(x)=3x7−6x6−10x4+3x3−15x−21f\left(x\right)=3x^7-6x^6-10x^4+3x^3-15x-21f(x)=3x7−6x6−10x4+3x3−15x−21

Create a free account and access millions of resources

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Popular Resources on Wayground

Discover more resources for Mathematics

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

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

The General Power Rule says that
$\frac{d}{dx}\left[x^n\right]=$

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

Find the derivative of:
$f\left(x\right)=\frac{3}{4}x-8$

Find the derivative:
$f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$

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

How do you rewrite this in power form:
$f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$

How can you change this to power form:
$f\left(x\right)=4\sqrt{x}$

Find the derivative of:
$f\left(x\right)=3x^7-6x^6-10x^4+3x^3-15x-21$