# Core 3

• Created by: Ellie
• Created on: 09-04-15 17:28
In the chain rule what is dy/dx?
dy/du x du/dx
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What are the laws of natural logarithms?
lna+lnb = lnab, lna-lnb=lna/b, lna^n = nlna, lne=1
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If y = uv what is the product rule?
dy/dx = u x dv/dx +v x du/dx
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Whats the quotient rule if y=u/v
(v x du/dx - u x dv/dx ) / v^2
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Differentiate y=lnx
dy/dx = 1/x
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Differentiate y = ln f(X)
dy/dx = f ' (x)/ f(x)
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Describe the cycle of differentiating trigonometry starting at sin x
sin x -> cos x -> -sin x -> - cos x
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What happens when you integrate e^(ax) dx?
1/a * e^(ax)+ c
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What happens when you integrate 1/x dx?
ln(x+c)
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What happens when you integrate f ' (x)/ f(x)?
ln(f(x)+c)
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How do you integrate by parts?
uv - integrated (v du/dx) dx
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Describe the transformation f(x)+a
a movement of a to the right
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Describe the transformation f(x+a)
a movement of a down
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Describe the transformation of af(x)
a vertical stretch with a scale factor of a (a times y coordinates)
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Describe the transformation f(ax)
a vertical stretch by scale factor of 1/a
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Describe the transformation -f(x)
a reflection in the x axis
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Describe the transformation f(-x)
a reflection in the y axis
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When is a function odd?
when f(-x) - -f(x)
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When is a function even?
When f(-x) = f(x)
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In graph terms when is a function even?
If its graph has a line of symmetry in the y axis
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In graph terms when is a function odd?
if its graph has rotational symmetry of order 2 about the origin
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Describe whether sin and cos are odd or even
sin is odd and cos is even
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What is a co domain?
all the possible outputs of a mapping
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What is a domain?
All the possible inputs of a mapping
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What is a range?
a set of images for a particular set of objects for a mapping
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When is something one to many?
when an object can be mapped to 2 or more images
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When is something one to one?
when an object can be matched to only one image
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What is arc sin arc cos and arc tan?
sin ^(-1) cos ^(-1) and tan ^(-1)
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When is a graph periodic?
If it has a repeating pattern
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## Other cards in this set

### Card 2

#### Front

What are the laws of natural logarithms?

#### Back

lna+lnb = lnab, lna-lnb=lna/b, lna^n = nlna, lne=1

### Card 3

#### Front

If y = uv what is the product rule?

#### Back ### Card 4

#### Front

Whats the quotient rule if y=u/v

#### Back ### Card 5

#### Front

Differentiate y=lnx

#### Back 