Calc 1 Review Basic Derivative Rules Flashcards

1

derivative of arctan(x)

\frac{1}{1+x^2}
\frac{1}{\sqrt{1-x^2}}
\frac{2x}{1+x^2}
-\frac{1}{\sqrt{1-x^2}}

2

find the velocity function from the position function f\left(t\right)=-16t^2+32t+65

32t=-32
f(t)=-32t+32
f(t)=-32

3

derivative of tan x

−csc2 x
sec2 x
tan x sec x
sec x

4

Find the derivative of 3^x

3x
1/3x
ln(3)3x
ln3

5

Derivative of sin(x)

\sin^{-1}\left(x\right)
csc(x)
-cos(x)
cos(x)

6

Derivative of cos(x)

csc x
sin x
tan x
-sin x

7

The derivative of velocity gives

position
displacement
acceleration
velocity

8

Derivative of \sqrt{x}

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

9

Derivative of cot(x)

sec2(x)
csc2(x)
-sec2x
-csc2(x)

10

derivative of arccos(x)

\frac{-1}{\sqrt{1-x^2}}
cos(sin(x))
\frac{1}{\sqrt{x^2+1}}
-arcsin(x)

11

What is the derivative of e^x?

e^x
\ln\left(x\right)
x\cdot e^{x-1}

12

Derivative of ln(x)

\frac{x}{1}
\frac{1}{x}
1
x ⋅ ln(e)

13

What is the formula for the chain rule? (f(g(x)))'=

f '(g(x))g'(x)
f(x)g'(x)+f '(x)g(x)
f '(g'(x))
f '(g(x))+g'(x)

14

Which of the following derivatives does not require the Chain Rule?

\frac{d}{dx}\left[e^{3x}\right]
\frac{d}{dx}\left[\sqrt{3x-1}\right]
\frac{d}{dx}\left[\sin^2\left(x\right)\right]
\frac{d}{dx}\left[\frac{1}{x^3}\right]

15

derivative of arcsec(x)

1/(ƖxƖ√(x2-1))
-1/(ƖxƖ√(x2-1))
1/√(1 - x2)
1/(ƖxƖ√(1-x2))

16

Technique to evaluate limits of indeterminate forms usually used in Calculus

Tessellation
L'Hopital Rule
Least Squares Method
LaPLace Transformations

17

Derivative of csc(x):

-csc(x)cot(x)
-csc(x)2
sec(x)2
sec(x)tan(x)

Calc 1 Review Basic Derivative Rules

Questions 17

Calc 1 Review Basic Derivative Rules

Questions 17