Calculus AB AP Unit 5 Formulas

Ln, log, exponents, Trig, and inverse Trig.

Derivative of ln(x)

$\frac{1}{x}$ dt for all $x > 0$. (x to 1)

Ln domain and range

The domain of $\text{ln}(x)$ is all positive real numbers, $x > 0$, and the range is all real numbers, $(-\text{∞}, \text{∞})$.

Ln (1)

The value of $\text{ln}(1)$ is 0, since the logarithm of 1 in any base is always zero.

Ln(x) is always

increasing, continuos, and concave down.

Ln (ab)

Ln(a)+ln(b)

Ln(a^n)

n*ln(a)

Ln(a/b)

ln(a)-Ln(b)

Intergral of 1/x dx

Ln |x| +c

Intergral of u prime over u du

Ln|u| + c

Intergral of tan

-ln|cosx| + C or Ln|secx| +C

Intergral for Cot

-Ln| cscx| + C

Intergral of sec

Ln|secx+tanx| + C

Intergral of csc

-Ln|cscx +cotx| + C

derivative of e^x

e^x

e^u derivative

U prime e^u

Intergral of e^x

e^x + C

a^x derivative

a^x Ln(a)

a^u derivative

U prime a^u Ln(a)

a^x intergral

a^x/Ln(a) + C

Derivative of Log

1/xLn(a)

derivative of Log (u)

U prime/ uLn(a)

y=f(x) is equal to

x=f inverse (y)

derivative of f inverse

1/f prime (f^-1 (x))

arcsin x derivative

1/sqrt(1-x²)

arccos x derivative

-1/sqrt(1-x²)

arctan x derivative

1/x²+1

arccot x derivative

-1/x²+1

arcsec x derivative

1/|x|sqrt(x²-1)

arccsc x derivative

-1/|x|sqrt(x²-1)

intergral of 1/sqrt(a²-u²) du

arcsin(u/a) + C

intergral of 1/a²+u² du

1/a arctan(u/a) + C