Maths Formulas Flashcards
Chain rule
Dy/dx = dy/du x du/dx
Product rule
Dy/dx = u(dv/dx) + v(du/dx). u and v are the constants
Quotient rule
dy/dx = v(du/dx) - u(du/dx) all divided by v squared ( remember v is the denominator)
Implicit differentiation
f(y) = f’(y) x dy/dx
Reciprocal of dy/dx
1/(dx/dy)
Parametric differentiation
Dy/dx = (dy/dt)/(dx/dt)
If f’(x) is less than 0, the function is …
Decreasing
If f’(x) is = 0, the function is…
Stationary
If f’(x) is greater than 0, the function is …
Increasing
If f’’(x) is less than 0, the point is…
Maximum - also concave
If f’’(x) is =0, the point is
A point of inflection
If f’’(x) is greater than 0, the point is…
Minimum - is convex
Derivative of e to the power of x
E to the power of x
Derivative of ln (x)
1/x
Derivative of sinx
Cosx
Derivative of cosx
-sinx
Derivative of tanx
sec squared x
Derivative of secx
secxtanx
Derivative of cotx
-cosec squared x
Derivative of cosecx
-cosecxcotx
How do you work out the other answers for sinx ?
180 - x / cos (90-x)
How do you work out the other answers for cosx?
360 - x / sin (90-x)
How do you work out the other answers for tanx?
X + 180
1 + tan squared x is = to ?
Sec squared x
1 + cot squared x is equal to?
Cosec squared x
Sin2x double angle formulae?
2sinxcosx
Cos2x double angle forumale?
Either cos squared x - sin squared x OR 2cos squared x - 1 OR 1 - 2 sin squared x
Tan2x double angle forumale?
2tanx/1- tan squared x
F(x) + a transformation
Y- direction moves up a
F(x+a) transformation
X direction moves left a (-a)
Af(x) transformation
Stretch y-direction by a
F(ax) transformation
Stretch x-direction by 1/a
-f(x) transformation
Reflection in the x-axis
F(-x) transformation
Reflection in the y-axis
/f(x)/ transformation
Anything below the x-axis goes up
f(/x/) transformation
Anything right of the y-axis goes left
Integral of cosx
Sinx
Integral of sinx
-cosx
Integral of sec squared x
Tanx
Integral of secxtanx
Secx
Integral of cosec squared x
-cotx
Integral of cosecxcotx
-cosecx
Integral of f’(ax+b)
1/af(ax+b)
Steps for the substitution rule
Find u, find du in terms of dx, change the limits to u
Integration by parts formula
uv- integral of (du/dx x v)
Parametric integration formula
Integral of y x dx/dt dt, change the limits
A to the power of n x A to the power of m
A to the power of n+m
A to the power of n/ A to the power of m
A to the power of n-m
(A to the power of n) to the power of m
A to the power of n x m
A to the power of -n
1/ a to the power of n
A to the power of 1/n
A to the root of n
A to the power of 0
1
Log a x = n
A to the power of x = n
Lnxy =
Lnx + lny
Ln x/y =
Lnx - lny
Lnx to the power of k
Klnx
Ln 1/x =
-lnx
Lne =
1
Ln1 =
0
Cosine rule
A squared = b squared + c squared - 2bccosA
Sine rule
SinA/a = SinB/b = SinC/c
Area of a triangle formula
1/2 x ab x sinC
Arc length
R x Theta
Area of a sector
1/2 x r squared x theta
Segment area
1/2 x r squared x (theta - sin theta )
Geometric nth term
Un = a x r to the power of n-1
Arithmetic nth term
Un = a + (n-1)d
Unit vector =
(1/ magnitude of a) x a
Volume of a sphere
4/3 pi x r cubed
Volume of a cylinder
Pi x r squared x h
Area of a cylinder
2 pi r h + 2 pi r squared
Area of a sphere
4 pi r squared
Integral of a to the power of x
A to the power of x lna
