Antiderivatives and Derivatives

Question 1

Find the antiderivative of x^n

Answer 1

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

Question 2

Find the antiderivative of sin(ax)

Answer 2

-cos(ax)/a +c

Question 3

Find the antiderivative of sec^2(ax)

Answer 3

tan(ax)/a +c

Question 4

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

Answer 4

sec(ax)/a +c

Question 5

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

Answer 5

-csc(ax)/a +c

Question 6

Find the antiderivative of e^ax

Answer 6

e^ax/a +c

Question 7

Find the antiderivative of 1/x

Answer 7

ln[x] +c

Question 8

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

Answer 8

sin^-1(ax)/a + c

Question 9

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

Answer 9

tan^-1(ax)/a +c

Question 10

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

Answer 10

sec^-1(ax)/a +c

Question 11

Find the antiderivative of a^(bx)

Answer 11

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

Question 12

Find the derivative of a

Answer 12

0

Question 13

Find the derivative of x

Answer 13

1

Question 14

Find the derivative of x^n

Answer 14

n*x^(n-1)

Question 15

Find the derivative of lnx

Answer 15

1/x

Question 16

Find the derivative of e^x

Answer 16

e^x

Question 17

Find the derivative of sinx

Answer 17

cosx

Question 18

Find the derivative of cosx

Answer 18

-sinx

Question 19

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

Answer 19

1/(1+x^2)

Question 20

What is quotient rule?

Answer 20

f’(x)g(x) - g’(x)f(x) / g(x)^2

Question 21

What is product rule?

Answer 21

f’(x)g(x) + g’(x)f(x)