Calc 2 Integration/derivation rules

Includes basics like the power rule, the chain rule, and the Exponential function rule, and some more complex rules, such as Integration by parts, Trig Identities, and formulas you might need for Calculus 2...

= 2Sin(ϴ)Cos(ϴ)

Sin(2ϴ) = ??? (Double Angle)

= Cos²(ϴ) - Sin²(ϴ)

Cos(2ϴ) = ??? (Double Angle)

= (2Tan(ϴ)) / (1 - Tan²(ϴ))

Tan(2ϴ) = ??? (Double Angle)

= 1

Sin²(ϴ) + Cos²(ϴ) = ??? (Pythagorean Identity)

= Sec²(ϴ)

1 + Tan²(ϴ) = ??? (Pythagorean Identity)

= Csc²(ϴ)

1 + Cot²(ϴ) = ??? (Pythagorean Identity)

The derivative is cos(x).

what is the derivative of sin(x)?

The derivative is -sin(x).

what is the derivative of cos(x)?

The derivative is sec²(x).

what is the derivative of tan(x)?

The derivative is -csc²(x).

what is the derivative of cot(x)?

The derivative is sec(x)tan(x).

what is the derivative of sec(x)?

The derivative is -csc(x)cot(x).

what is the derivative of csc(x)?

The integral is -cos(x) + C.

what is the integral of sin(x)?

The integral is sin(x) + C.

what is the integral of cos(x)?

The integral is tan(x) + C.

what is the integral of sec²(x)?

The integral is -cot(x) + C.

what is the integral of csc²(x)?

The integral is sec(x) + C.

what is the integral of sec(x)tan(x)?

The integral is -csc(x) + C.

what is the integral of csc(x)cot(x)?

The integral is -ln|cos(x)| + C, or ln|sec(x)| + C.

what is the integral of tan(x)?

The integral is ln|sin(x)| + C, or -ln|csc(x)| + C.

what is the integral of cot(x)?

The integral is ln|sec(x) + tan(x)| + C.

what is the integral of sec(x)?

The integral is -ln|csc(x) + cot(x)| + C.

what is the integral of csc(x)?

The derivative is 1 / √(1 - u²) * u’

what is the derivative of arcsin(u)?

what is the derivative of arccos(u)?

The derivative is 1 / (1 + u²) * u'.

what is the derivative of arctan(u)?

The derivative is 1 / |u| √(u² - 1) * u'.

what is the derivative of arcsec(u)?

The derivative is -1 / |u| √(u² - 1) * u'.

what is the derivative of arccsc(u)?

The derivative is -1 / (1 + u²) * u'.

what is the derivative of arccot(u)?

The power rule for integration states that the integral of u^n is (u^(n+1))/(n+1) + C, where n ≠ -1.

what is the power rule (integration)

The power rule for differentiation states that the derivative of u^n is n * u^(n-1) * u', where n is any real number.

what is the power rule (derivation)

The chain rule states that the derivative of a composite function f(g(u)) is f'(g(u)) * g'(u).

what is the chain rule?

the integral of u*v’ = u*v + the integral of v*u’

integration by parts, aka the Ulta Violet Voodoo Method

u*v + the integral of v*u’

the integral of u*v’ = ???

the derivative is 1 / x.

what is the derivative of ln(x)?

the integral is ln(x).

what is the integral of 1 / x?

the derivative is n^x(ln(x))

what is the derivative of n^x?

the integral is n^x / ln(n)

what is the integral of n^x?