Maths Formulas Flashcards by Archie Kemp | Brainscape

Q

Chain rule

A

Dy/dx = dy/du x du/dx

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Q

Product rule

A

Dy/dx = u(dv/dx) + v(du/dx). u and v are the constants

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Q

Quotient rule

A

dy/dx = v(du/dx) - u(du/dx) all divided by v squared ( remember v is the denominator)

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Q

Implicit differentiation

A

f(y) = f’(y) x dy/dx

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Q

Reciprocal of dy/dx

A

1/(dx/dy)

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Q

Parametric differentiation

A

Dy/dx = (dy/dt)/(dx/dt)

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Q

If f’(x) is less than 0, the function is …

A

Decreasing

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Q

If f’(x) is = 0, the function is…

A

Stationary

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Q

If f’(x) is greater than 0, the function is …

A

Increasing

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Q

If f’’(x) is less than 0, the point is…

A

Maximum - also concave

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Q

If f’’(x) is =0, the point is

A

A point of inflection

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Q

If f’’(x) is greater than 0, the point is…

A

Minimum - is convex

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Q

Derivative of e to the power of x

A

E to the power of x

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Q

Derivative of ln (x)

A

1/x

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Q

Derivative of sinx

A

Cosx

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Q

Derivative of cosx

A

-sinx

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Q

Derivative of tanx

A

sec squared x

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Q

Derivative of secx

A

secxtanx

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Q

Derivative of cotx

A

-cosec squared x

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Q

Derivative of cosecx

A

-cosecxcotx

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Q

How do you work out the other answers for sinx ?

A

180 - x / cos (90-x)

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Q

How do you work out the other answers for cosx?

A

360 - x / sin (90-x)

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Q

How do you work out the other answers for tanx?

A

X + 180

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Q

1 + tan squared x is = to ?

A

Sec squared x

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Q

1 + cot squared x is equal to?

A

Cosec squared x

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Q

Sin2x double angle formulae?

A

2sinxcosx

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Q

Cos2x double angle forumale?

A

Either cos squared x - sin squared x OR 2cos squared x - 1 OR 1 - 2 sin squared x

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Q

Tan2x double angle forumale?

A

2tanx/1- tan squared x

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Q

F(x) + a transformation

A

Y- direction moves up a

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Q

F(x+a) transformation

A

X direction moves left a (-a)

Q

Af(x) transformation

A

Stretch y-direction by a

Q

F(ax) transformation

A

Stretch x-direction by 1/a

Q

-f(x) transformation

A

Reflection in the x-axis

Q

F(-x) transformation

A

Reflection in the y-axis

Q

/f(x)/ transformation

A

Anything below the x-axis goes up

Q

f(/x/) transformation

A

Anything right of the y-axis goes left

Q

Integral of cosx

A

Sinx

Q

Integral of sinx

A

-cosx

Q

Integral of sec squared x

A

Tanx

Q

Integral of secxtanx

A

Secx

Q

Integral of cosec squared x

A

-cotx

Q

Integral of cosecxcotx

A

-cosecx

Q

Integral of f’(ax+b)

A

1/af(ax+b)

Q

Steps for the substitution rule

A

Find u, find du in terms of dx, change the limits to u

Q

Integration by parts formula

A

uv- integral of (du/dx x v)

Q

Parametric integration formula

A

Integral of y x dx/dt dt, change the limits

Q

A to the power of n x A to the power of m

A

A to the power of n+m

Q

A to the power of n/ A to the power of m

A

A to the power of n-m

Q

(A to the power of n) to the power of m

A

A to the power of n x m

Q

A to the power of -n

A

1/ a to the power of n

Q

A to the power of 1/n

A

A to the root of n

Q

A to the power of 0

A

1

Q

Log a x = n

A

A to the power of x = n

Q

Lnxy =

A

Lnx + lny

Q

Ln x/y =

A

Lnx - lny

Q

Lnx to the power of k

A

Klnx

Q

Ln 1/x =

A

-lnx

Q

Lne =

A

1

Q

Ln1 =

A

0

Q

Cosine rule

A

A squared = b squared + c squared - 2bccosA

Q

Sine rule

A

SinA/a = SinB/b = SinC/c

Q

Area of a triangle formula

A

1/2 x ab x sinC

Q

Arc length

A

R x Theta

Q

Area of a sector

A

1/2 x r squared x theta

Q

Segment area

A

1/2 x r squared x (theta - sin theta )

Q

Geometric nth term

A

Un = a x r to the power of n-1

Q

Arithmetic nth term

A

Un = a + (n-1)d

Q

Unit vector =

A

(1/ magnitude of a) x a

Q

Volume of a sphere

A

4/3 pi x r cubed

Q

Volume of a cylinder

A

Pi x r squared x h

Q

Area of a cylinder

A

2 pi r h + 2 pi r squared

Q

Area of a sphere

A

4 pi r squared

Q

Integral of a to the power of x

A

A to the power of x lna