Antiderivatives and Derivatives Flashcards Preview

MATH 1552: Integral Calculus > Antiderivatives and Derivatives > Flashcards

Flashcards in Antiderivatives and Derivatives Deck (21)
Loading flashcards...
1
Q

Find the antiderivative of x^n

A

(x^(n+1))/(n+1) +c

2
Q

Find the antiderivative of sin(ax)

A

-cos(ax)/a +c

3
Q

Find the antiderivative of sec^2(ax)

A

tan(ax)/a +c

4
Q

Find the antiderivative of sec(ax)tan(ax)

A

sec(ax)/a +c

5
Q

Find the antiderivative of csc(ax)cot(ax)

A

-csc(ax)/a +c

6
Q

Find the antiderivative of e^ax

A

e^ax/a +c

7
Q

Find the antiderivative of 1/x

A

ln[x] +c

8
Q

Find the antiderivative of 1/sqrt(1+(ax)^2)

A

sin^-1(ax)/a + c

9
Q

Find the antiderivative of 1/1+(ax)^2

A

tan^-1(ax)/a +c

10
Q

Find the antiderivative of 1/x*sqrt((ax^2)-1)

A

sec^-1(ax)/a +c

11
Q

Find the antiderivative of a^(bx)

A

a^(bx)/b*ln(a) +c

12
Q

Find the derivative of a

A

0

13
Q

Find the derivative of x

A

1

14
Q

Find the derivative of x^n

A

n*x^(n-1)

15
Q

Find the derivative of lnx

A

1/x

16
Q

Find the derivative of e^x

A

e^x

17
Q

Find the derivative of sinx

A

cosx

18
Q

Find the derivative of cosx

A

-sinx

19
Q

Find the derivative of tan^-1(x) (also known as arctan(x)

A

1/(1+x^2)

20
Q

What is quotient rule?

A

f’(x)g(x) - g’(x)f(x) / g(x)^2

21
Q

What is product rule?

A

f’(x)g(x) + g’(x)f(x)