Find the derivative: h ( x ) = x − 2 x h\left(x\right)=\sqrt{x}-2x h ( 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 x

h ′ ( x ) = 1 2 x − 2 h'\left(x\right)=\frac{1}{2\sqrt{x}}-2 h ′ ( 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"> 1 − 2

h ′ ( x ) = 1 2 x + 2 h'\left(x\right)=\frac{1}{2\sqrt{x}}+2 h ′ ( 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"> 1 + 2

h ′ ( x ) = − 1 2 x − 2 h'\left(x\right)=-\frac{1}{2\sqrt{x}}-2 h ′ ( 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"> 1 − 2

h ′ ( x ) = 1 x − 2 h'\left(x\right)=\frac{1}{\sqrt{x}}-2 h ′ ( 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"> 1 − 2

h ( x ) = e x cos ⁡ x h\left(x\right)=e^x\cos x h ( x ) = e x cos x Find the derivative.

h ′ ( x ) = e x cos ⁡ x − e x sin ⁡ x h'\left(x\right)=e^x\cos x-e^x\sin x h ′ ( x ) = e x cos x − e x sin x

h ′ ( x ) = e x − 1 cos ⁡ x − e x sin ⁡ x h'\left(x\right)=e^{x-1}\cos x-e^x\sin x h ′ ( x ) = e x − 1 cos x − e x sin x

h ′ ( x ) = e x cos ⁡ x + e x sin ⁡ x h'\left(x\right)=e^x\cos x+e^x\sin x h ′ ( x ) = e x cos x + e x sin x

h ′ ( x ) = − e x sin ⁡ x h'\left(x\right)=-e^x\sin x h ′ ( x ) = − e x sin x

Calculus Derivatives #2

Quiz

•

Mathematics

•

11th Grade - University

•

Practice Problem

•

Medium

•

CCSS

HSF.IF.A.2, HSN.RN.A.1, HSA.APR.D.7

Standards-aligned

Adam Hosler

Used 39+ times

FREE Resource

14 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative:
$f\left(x\right)=12x^3-9x^2+11x-2$

$f'\left(x\right)=36x^2-18x+11$

$f'\left(x\right)=36x^2-81x+11$

$f'\left(x\right)=12x^2-9x+11$

$f'\left(x\right)=36x^2+18x-11$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative:
$g\left(x\right)=\frac{1}{x}-\frac{1}{x^2}$

$g'\left(x\right)=-\frac{1}{x^2}+\frac{2}{x^3}$

$g'\left(x\right)=\frac{1}{x^2}+\frac{2}{x^3}$

$g'\left(x\right)=-\frac{1}{x^2}-\frac{2}{x^3}$

$g'\left(x\right)=-\frac{1}{x^2}+\frac{1}{x^3}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative:

$h\left(x\right)=\sqrt{x}-2x$

$h'\left(x\right)=\frac{1}{2\sqrt{x}}-2$

$h'\left(x\right)=\frac{1}{2\sqrt{x}}+2$

$h'\left(x\right)=-\frac{1}{2\sqrt{x}}-2$

$h'\left(x\right)=\frac{1}{\sqrt{x}}-2$

Find the derivative:
$f\left(x\right)=x^2\sin x$

$f'\left(x\right)=2x\sin x+x^2\cos x$

$f'\left(x\right)=2x\sin x-x^2\cos x$

$f'\left(x\right)=-2x\sin x+x^2\cos x$

$f'\left(x\right)=2x\cos x$

Find the derivative:
$g\left(x\right)=\sec x\tan x$

$g'\left(x\right)=\sec x\tan^2x+\sec^3x$

$g'\left(x\right)=\sec x\tan^2x-\sec^3x$

$g'\left(x\right)=-\sec x\tan^2x+\sec^3x$

$g'\left(x\right)=\sec x\tan x\sec^2x=\sec^3x\tan x$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$h\left(x\right)=e^x\cos x$
Find the derivative.

$h'\left(x\right)=e^x\cos x-e^x\sin x$

$h'\left(x\right)=e^{x-1}\cos x-e^x\sin x$

$h'\left(x\right)=e^x\cos x+e^x\sin x$

$h'\left(x\right)=-e^x\sin x$

Find the derivative:
$f\left(x\right)=\frac{x^2}{x-3}$

$f'\left(x\right)=\frac{x^2-6x}{\left(x-3\right)^2}$

$f'\left(x\right)=\frac{x^2+6x}{\left(x-3\right)^2}$

$f'\left(x\right)=\frac{x^2-6x}{\left(x-3\right)^3}$

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

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Calculus Derivatives #2

14 questions

Find the derivative:
$f\left(x\right)=12x^3-9x^2+11x-2$

Find the derivative:
$g\left(x\right)=\frac{1}{x}-\frac{1}{x^2}$

Find the derivative:

$h\left(x\right)=\sqrt{x}-2x$

Find the derivative:
$f\left(x\right)=x^2\sin x$

Find the derivative:
$g\left(x\right)=\sec x\tan x$

$h\left(x\right)=e^x\cos x$
Find the derivative.

Find the derivative:
$f\left(x\right)=\frac{x^2}{x-3}$

Find the derivative:
$f\left(x\right)=\frac{x+3}{x-1}$

Find the derivative:
$f\left(x\right)=\frac{x}{\sin x}$

Find the derivative:
$f\left(x\right)=\left(x^2-3\right)^{10}$

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Calculus Derivatives #2

14 questions

Find the derivative: f(x)=12x3−9x2+11x−2f\left(x\right)=12x^3-9x^2+11x-2f(x)=12x3−9x2+11x−2

Find the derivative: g(x)=1x−1x2g\left(x\right)=\frac{1}{x}-\frac{1}{x^2}g(x)=x1​−x21​

Find the derivative: h(x)=x−2xh\left(x\right)=\sqrt{x}-2xh(x)=x​−2x

Find the derivative: f(x)=x2sin⁡xf\left(x\right)=x^2\sin xf(x)=x2sinx

Find the derivative: g(x)=sec⁡xtan⁡xg\left(x\right)=\sec x\tan xg(x)=secxtanx

h(x)=excos⁡xh\left(x\right)=e^x\cos xh(x)=excosx Find the derivative.

Find the derivative: f(x)=x2x−3f\left(x\right)=\frac{x^2}{x-3}f(x)=x−3x2​

Find the derivative: f(x)=x+3x−1f\left(x\right)=\frac{x+3}{x-1}f(x)=x−1x+3​

Find the derivative: f(x)=xsin⁡xf\left(x\right)=\frac{x}{\sin x}f(x)=sinxx​

Find the derivative: f(x)=(x2−3)10f\left(x\right)=\left(x^2-3\right)^{10}f(x)=(x2−3)10

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Discover more resources for Mathematics

Find the derivative:
$f\left(x\right)=12x^3-9x^2+11x-2$

Find the derivative:
$g\left(x\right)=\frac{1}{x}-\frac{1}{x^2}$

Find the derivative:

$h\left(x\right)=\sqrt{x}-2x$

Find the derivative:
$f\left(x\right)=x^2\sin x$

Find the derivative:
$g\left(x\right)=\sec x\tan x$

$h\left(x\right)=e^x\cos x$
Find the derivative.

Find the derivative:
$f\left(x\right)=\frac{x^2}{x-3}$

Find the derivative:
$f\left(x\right)=\frac{x+3}{x-1}$

Find the derivative:
$f\left(x\right)=\frac{x}{\sin x}$

Find the derivative:
$f\left(x\right)=\left(x^2-3\right)^{10}$