Differential Calculus Poster

Differential Calculus Poster

2nd Parcial project - 1st Part

Constant RulE

d --- [ c ] = 0 dx

c is a constant

f ( x ) = c

f ' ( x ) = 0

Constant Multiple Rule

d d-- [k * f (x)] = k* -- f (x)dx dx

Addition/Subtraction Rule

d d d-- [f (x) + g (x)] = -- f (x) + -- g (x) dx dx dx

d d d-- [f (x) - g (x)] = -- f (x) - -- g (x) dx dx dx

product Rule

F (x) * g (x)= ( f (x) * g (x) ) ' = f' (x) * g (x) + g ' (x) * f (x)

( f * g)' = f' *g + f * g'

Derivative of the first times the second plus the derivative of the second times the first.

Power Rule

d -- [x ^ n] = n * x ^ n - 1 dx

Differential Calculus Poster

2nd Parcial project - 1st Part

Quotient Rule

( f (x)' f' * g - f * g' ---- = --------- ( g (x) g2

Exponential/Logarithmic Functions( xe and ln( )x)

h (x) = x ^ - 1 = 1 -- x

f (x) = x ^ 2

g (x) = x ^ 1 -- = √2 2

Trigonometric Functions (sine and cosine)

Tangent TAN (0) = a -- 0

Cosine COS (0) = d -- c

Sine SIN (0) = a -- c

Differential Calculus Poster

2nd Parcial project - 1st Part

Tangent & Normal Lines with a picture or a graph.

The derivative of a function at a point is the slope of the tangent line at that point. The normal line is defined as the perpendicular line to the tangent.

The slopes of perpendicular lines are negative reciprocals of one another so the slope of the normal line to the graph of f(x) = −1/ f′(x).

Example of a calculus problem with the steps

3x + 1 y= ------ 2x^4

d ( 3x 1 ) d ( 3x 1 ) --= ----- + ---- = -- ---- + ----- dx ( 2x^4 2x^4) dx ( 2x^4 2x^4 )

d ( 3 ) 3 d ( 1 ) 3x + 1 --= ----- = --- x^-3 + -- ----- = ----- dx ( 2x^3 ) 2 dx ( 2x^4 ) 2x^3

3x + 1y'= ----- 2x^3

Final