Derivatives and Antiderivatives (copy)

Antiderivative of f(x) = x^n

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

Antiderivative of f(x) = 1/x

ln|x| + C

Antiderivative of f(x) = e^x

e^x + C

Antiderivative of f(x) = sin(x)

-cos(x) + C

Antiderivative of f(x) = cos(x)

sin(x) + C

Antiderivative of f(x) = sec^2(x)

tan(x) + C

Antiderivative of f(x) = csc^2(x)

-cot(x) + C

Antiderivative of f(x) = 1/(sqrt(1-x^2))

arcsin(x) + C

Antiderivative of f(x) = 1/(1+x^2)

arctan(x) + C

Antiderivative of f(x) = a^x

(a^x)/(ln(a)) + C

Antiderivative of f(x) = sec(x)tan(x)

sec(x) + C

Antiderivative of f(x) = csc(x)cot(x)

-csc(x) + C

Derivative of F(x) = k

F(x) = 0

Derivative of F(x) = x

F'(x) = 1

Derivative of F(x) = x^2

F'(x) = 2x

Derivative of F(x) = x^3

F'(x)=3x^2

Derivative of F(x) = sin(x)

F'(x) = cos(x)

Derivative of F(x) = ln(x)

F'(x) = 1/x

Derivative of F(x) = e^x

F'(x) = e^x

Derivative of F(x) = x^n

F'(x) = nx^(n-1)

Derivative of F(x) = |x|

F'(x) = x/|x|, x =/= 0

Derivative of F(x) = 1/(x^n)

F'(x) = -nx^-(n+1)

Derivative of F(x) = sqrt(x)

F'(x) = x^(1/2) = 1/2(x)^(-1/2) = 1/(2(sqrt(x)), x>0

Derivative of F(x) = e^x

F'(x) = e^x

Derivative of F(x) = a^x

F'(x) = (a^x)(ln(a))

Derivative of F(x) = x^x

F'(x) = (x^x)(1+ln(x))

Derivative of F(x) = log(sub(a))(x)

F'(x) = 1/(xln(a))

Derivative of F(x) = cos(x)

F'(x) = -sin(x)

Derivative of F(x) = tan(x)

F'(x) = sec^2(x) = 1/(cos^2(x))

Derivative of F(x) = sec(x)

F'(x) = sec(x)tan(x)

Derivative of F(x) = csc(x)

F'(x) = -csc(x)cot(x)

Derivative of F(x) = cot(x)

F'(x) = -csc^2(x)

Derivative of F(x) = arcsin(x)

F'(x) = 1/(sqrt(1-x^2))

Derivative of F(x) = arccos(x)

F'(x) = -1/(sqrt(1-x^2))

Derivative of F(x) = arctan(x)

F'(x) = 1/(1+x^2)

Derivative of F(x) = arccot(x)

-1/(1+x^2)

Derivative of F(x) = arcsec(x)

1/(x(sqrt((x^2)-1))

Derivative of F(x) = arccsc(x)

-1/(x(sqrt((x^2)-1))