Calculus I (Derivative Bible)

Front 1

Derivative of a constant times a function

Back 1

D(c f(x) ) / d(x) = C • f'(x)

Front 2

Derivative of a constant

Back 2

Always zero

Front 3

Derivative of a power

Back 3

d(x^n) / d(x) = n(X)^ n-1

Front 4

Derivative of the sum/difference of 2 functions

Back 4

d( f(x) + g(x) ) / d(x) = f'(x) + g'(x)
d( f(x) - g(x) ) / d(x) = f'(x) - g'(x)

Front 5

Product rule

Back 5

d( f o g) (x) / d(x) =
f(x)•g'(x) + g(x)•f'(x) =
1st • derivative of 2nd + 2nd • derivative of 1st

Front 6

Quotient rule

Back 6

d( f/g) (x) / d(x) =
g(x) • f'(x) - f(x) • g'(x) \ (g(x))^2
Bottom•derivative of top - top•derivative of bottom / bottom^2

Hint 6

B•T' - T•B' / B^2

Front 7

Derivative of sine

Back 7

d(sin x) / dx = cos x

Front 8

Derivative of cosine

Back 8

d(cos x) / dx = -sin x

Hint 8

Name starts with c - derivative is negative

Front 9

Derivative of tangent

Back 9

d(tan x) / dx = sec ^2 x

Front 10

Derivative of secant

Back 10

d(sec x) / dx = sec x tan x

Front 11

Derivative of cosecant

Back 11

d(csc x) / dx = -csc x cot x

Hint 11

Name starts with c - derivative is negative

Front 12

Derivative of cotangent

Back 12

d(cot x) / dx = -csc ^2 x

Hint 12

Name starts with c - derivative is negative

Front 13

Chain rule

Back 13

h(x) = f (g(x)) =
h'(x) = f' ( g(x) ) • g'(x)
•Derivative of outside function •evaluated at the inside function in parenthesis
•multiplied by derivative of inside function

Front 14

Definition of derivative

Back 14

lim ( f(w) - f(x) / w-x )
w->x

lim ( f(x+h) - f(x) / h )
h->0