Find the derivative of f(x) = 6x 30 -2x 15 + 4x 3 - 2x + 1

f'(x) = 180x 29 - 30x 14 + 12x 2 - 2

f'(x) = 18x 29 + 30x 15 + 12x 3

f'(x) = 180x 29 - 30x 14 + 12x 2

f'(x) = 180x 29 - 30x 14 + 12x 2 +1

Find the derivative of f ( x ) = ( 3 − x ) ( 3 − x ) f\left(x\right)\ =\ \left(3\ -\ \sqrt{x}\right)\left(3\ -\ \sqrt{x}\right) f ( x ) = ( 3 − 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"> ) ( 3 − 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"> )

− 3 x − 1 -\frac{3}{\sqrt{x}}-1 − 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"> 3 − 1

9 − 6 x − x 9-6\sqrt{x}-x 9 − 6 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"> − x

− 1 3 x − 1 -\frac{1}{3\sqrt{x}}-1 − 3 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"> 1 − 1

− 1 3 x − 1 -\frac{1}{\sqrt{3x}}-1 − 3 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"> 1 − 1

Derivatives The Power Rule

Authored by Kathleen Strunk

Mathematics

12th Grade

CCSS covered

Used 210+ times

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative of: f(x) = 4x⁴-3x³-9

16x⁴-9x³

16x⁴-9x³-0

16x³-9x²-9

16x³-9x²

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

$\frac{1}{2}x^2$

$\frac{1}{2\sqrt{x}}$

$\frac{1}{\sqrt{x}}$

$\frac{1}{2x^2}$

Find the derivative of $f\left(x\right)\ =\ \frac{1}{x^5}$

$5x^4$

$-5x^6$

$-\frac{5}{x^6}$

$\frac{1}{5x^6}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative of $f\left(x\right)\ =\ \frac{1}{2\sqrt{x}}$

$-\frac{1}{4\sqrt{x^3}}$

$-\frac{1}{\sqrt{x^3}}$

$-x^2$

$-4x^2$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Find the derivative of the given equation
f(x) = x³ + x² + 3

3x² + 2x

3x + 2x

3x + 2x + 3

x³ + x²

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

Find the derivative of $f\left(x\right)\ =\ \left(3\ -\ \sqrt{x}\right)\left(3\ -\ \sqrt{x}\right)$

$9-6\sqrt{x}-x$

$-\frac{3}{\sqrt{x}}-1$

$-\frac{1}{3\sqrt{x}}-1$

$-\frac{1}{\sqrt{3x}}-1$

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Derivatives The Power Rule

Find the derivative of: f(x) = 4x4-3x3-9

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

Find the derivative of f(x) = 1x5f\left(x\right)\ =\ \frac{1}{x^5}f(x) = x51​

Find the derivative of f(x) = 12xf\left(x\right)\ =\ \frac{1}{2\sqrt{x}}f(x) = 2x​1​

Find the derivative of the given equationf(x) = x3 + x2 + 3

Find the derivative of f(x) = 6x30 -2x15 + 4x3 - 2x + 1

Find the derivative of f(x) = (3 − x)(3 − x)f\left(x\right)\ =\ \left(3\ -\ \sqrt{x}\right)\left(3\ -\ \sqrt{x}\right)f(x) = (3 − x​)(3 − x​)

Find the derivative of the following:

Find the derivative of:

Find the derivative of:

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Find the derivative of: f(x) = 4x⁴-3x³-9

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

Find the derivative of $f\left(x\right)\ =\ \frac{1}{x^5}$

Find the derivative of $f\left(x\right)\ =\ \frac{1}{2\sqrt{x}}$

Find the derivative of the given equation
f(x) = x³ + x² + 3

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

Find the derivative of $f\left(x\right)\ =\ \left(3\ -\ \sqrt{x}\right)\left(3\ -\ \sqrt{x}\right)$