Derivatives - Calculus AB

Derivatives to memorize for Calc AB

f(x) = sin(x); f'(x) = ?

cos(x)

f(x) = cos(x); f'(x) = ?

-sin(x)

f(x) = tan(x); f'(x) = ?

sec²(x)

f(x) = cot(x); f'(x) = ?

-csc²(x)

f(x) = sec(x); f'(x) = ?

sec(x) tan(x)

f(x) = csc(x); f'(x) = ?

-csc(x) cot(x)

f(x) = eˣ; f'(x) = ?

eˣ

f(x) = ln |x| or f(x) = ln(x); f'(x) = ?

1
---
x

f(x) = constant; f'(x) = ?

0

f(x) = x; f'(x) = ?

1

f(x) = axⁿ; f'(x) = ?

n ax⁽ⁿ⁻¹⁾

f(x) = √x ; f'(x) = ?

1
----
2√x

f(x) = sin⁻¹(x) ; f'(x) = ?

1
-------
√(1-x²)

f(x) = cos⁻¹(x) ; f'(x) = ?

-1
-------
√(1-x²)

f(x) = tan⁻¹(x) ; f'(x) = ?

1
-------
1 + x²

f(x) = aˣ; f'(x) = ?

aˣ ln(a)

f(x) = logₐx; f'(x) = ?

1
-------
x ln(a)

...........1
f(x) = ----- ; f'(x) = ?
...........x

-1
---
x²

f(x) = h(x) - g(x); f'(x) = ?

h'(x) - g