differentiation Flashcards by Alia M | Brainscape

Q

d/dx

A

differentiation symbol

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Q

A

polynomial

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Q

d/dx(polynomial)

A

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Q

A

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Q

d/dx(X)

A

1

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Q

d/dx(1/x)

A

-1/x^2

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Q

d/dx(-1/x)

A

1/x^2

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Q

d/dx(3)

A

0

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Q

1/ square root of x

A

x^-1/2

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Q

1/x can be written as

A

x^-1

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Q

d/dx(ax+b)^n

A

n(ax+b)^n-1 * a

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Q

d/dx( square root ax+b)

A

1/2square root ax+b * a

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Q

dy/dx is AKA

A

f’(X)

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Q

tangent and normal are

A

perpendicular to eachother m1 * m2 = -1

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Q

equation of a line

A

y-y1=m(x-x1)

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Q

the chain rule is used for

A

3 variables

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Q

d/dt

A

rate of change

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Q

if y= f(X)

A

dy/dt= dy/dx * dx/dt

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Q

if v=f(l)

A

v/t = v/l * l/t so v=l^3

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Q

if A=f(r)

A

A/t= A/r * r/t so A=Pir^2

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Q

if dy/dt is positive

A

its said that y increases at t increases

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Q

if dy/dt is negative

A

its said that y decreases as t decreases

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Q

dy/dt=

A

rate of change of y

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Q

the gradient of stationary points

A

0

Q

stationary value

A

y coordinate of turning point

Q

stationary point

A

min and max turning point

Q

to find nature of stationary points and values

A

use second deravitive

Q

d^2y/dx^2

A

second derivative AKA f’‘(x)

Q

if d^2y/dx^2 is +ve

A

its a min point

Q

if d^2y/dx^2 is -ve

A

max TP

Q

sphere volume

A

Q

SA of a sphere

A

Q

hemisphere volume

A

Q

closed hemisphere SA

A

Q

open hemisphere SA

A

Q

cube volume

A

l^3

Q

cube surface area

A

6l^3

Q

cuboid volume

A

lbh

Q

cuboid closed SA

A

Q

cuboid open SA

A

Q

cone volume

A

Q

cone curved surface area

A

Q

cone surface area

A

Q

slant length of cone=

A

square root h^2 +r^2

Q

A

cone

Q

for similar cones

A

Q

cylinder volume

A

Q

cylinder curved surface area

A

Q

cylinder total closed surface area

A

Q

cylinder open total surface area

A

Q

prism volume

A

Q

prism TSA

A

Q

prism perimeter

A

Q

A

prism

Q

pyramid volume

A

1/3 * base area * hieght

Q

pyramid TSA

A

Q

A

Q

A