Calculus II Integrals and Derivatives

Product Rule

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

Quotient Rule

g(x)f'(x)-f(x)g'(x)/g(x)^2

Chain Rule

f'[g(x)]g'(x)

Derivative of sin(x)

cos(x)

Derivative of cos(x)

-sin(x)

Derivative of tan(x)

(secx)^2

Derivative of sec(x)

sec(x)tan(x)

Derivative of csc(X)

-csc(x)cot(x)

Derivative of cot(x)

-(cscx)^2

Derivative of arcsin(x)

1/√(1-x^2)

Derivative of arccos(x)

- 1/√(1-x^2)

Derivative of arctan(X)

1/(1+x^2)

Derivative of arcsec(x)

1/(|x|√(x)^2 -1)

Derivative of arccsc(x)

1/(|x|√(x)^2 -1)

Derivative of arccot(x)

-1/(1+x^2)

Derivative of (a)^x

(a)^x ln(a)

Derivative of e^x

e^x

Derivative of ln(x)

1/x where x>0

Derivative of ln|x|

1/x where x≠0

(logₐ(x))

1/[xln(a)] , x > o

Intergral of cos(x)dx

sin(x)+c

Intergral of sin(x)dx

-cos(x)+c

Intergral of [(secx)^2]dx

tan(x)+c

Intergral of sec(x)tan(x)dx

sec(x)+c

Intergral of csc(x)cot(x)dx

-csc(x)+c

Intergral of [(cscx)^2]dx

-cot(x)+c

Intergral of tan(x)dx

ln|sec(x)|+c

Intergral of cot(x)dx

ln|sin(x)|+c

Intergral of sec(x)dx

ln|sec(x)+tan(x)|+c

Intergral of ([sec(x)]^3) dx

(1/2)(sec(x)tan(x) + ln|sec(x)+tan(x)|)+c

Intergral of csc(x)dx

ln|csc(x) - cot(x)|+c

Intergral of ([csc(x)]^3)dx

(1/2)(-csc(x)cot(x)+ln|csc(x)-cot(x)|)+c