d y d x \frac{\text{d}y}{\text{d}x} d x d y

Definition of Derivatives

Authored by David Granda

Mathematics

11th Grade - University

CCSS covered

Used 56+ times

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15 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Derivative means the same thing as

slope of the tangent line

slope of the normal line

exponent

potato

Tags

CCSS.HSS.ID.C.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The derivative of a function is its

Slope

Maximum/Minimum

Instantaneous rate of change

Common Denominator

Tags

CCSS.HSF.IF.B.4

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

15x²

(5/4)x⁴

indeterminate

∞

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

MULTIPLE SELECT QUESTION

15 mins • 1 pt

f'(x)=

$\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$

$\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

$\frac{\text{d}y}{\text{d}x}$

an equation for the slope of the tangent line

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

$5x^2$

$10x$

DNE

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)$

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\lim_{x\rightarrow\infty}x^2+3x-5$

$-\infty$

$\infty$

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\lim_{x\rightarrow\infty}\left(\frac{x^2+x-3}{x^4-x^3+1}\right)$

$-\infty$

$\infty$

Tags

CCSS.HSA.APR.D.7

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Definition of Derivatives

Derivative means the same thing as

The derivative of a function is its

f'(x)=

lim⁡h→0(5(x+h)2−5x2h)\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)h→0lim​(h5(x+h)2−5x2​)

lim⁡x→2(x2−4x−2)\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)x→2lim​(x−2x2−4​)

lim⁡x→∞x2+3x−5\lim_{x\rightarrow\infty}x^2+3x-5x→∞lim​x2+3x−5

lim⁡x→∞(x2+x−3x4−x3+1)\lim_{x\rightarrow\infty}\left(\frac{x^2+x-3}{x^4-x^3+1}\right)x→∞lim​(x4−x3+1x2+x−3​)

If a function has a derivative that is negative, what does that tell you?

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$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

$\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)$

$\lim_{x\rightarrow\infty}x^2+3x-5$

$\lim_{x\rightarrow\infty}\left(\frac{x^2+x-3}{x^4-x^3+1}\right)$