Ap Calculus AB - Unit 3 Review

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10 Terms

1
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chain rule

d/dx[f(x)gx)] = f’[g(x)]*g’(x)

<p>d/dx[f(x)gx)] = f’[g(x)]*g’(x)</p>
2
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implicit differentiation

Take the derivative like normal except for anything except any variable that is not based on x, then take derivative in context of the variable. For example, d/dx(5y²) → 10y*dy/dx

<p>Take the derivative like normal except for anything except any variable that is not based on x, then take derivative in context of the variable. For example, d/dx(5y²) → 10y*dy/dx</p>
3
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Inverse derivatives

Function must be invertible and differentiable.
If f(x)=0, then the inverse function is differentiable, and the inverse of the derivative of the original function is equal to the derivative of the inverse function.

4
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d/dx[arcsin(u)]

u’/sqrt(1-u²)

<p>u’/sqrt(1-u²)</p>
5
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d/dx[arccos(u)]

-u’/sqrt(1-u²)

<p>-u’/sqrt(1-u²)</p>
6
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d/dx[arctan(u)]

u’/1-u²

<p>u’/1-u²</p>
7
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d/dx[arccot(u)]

-u’/1-u²

<p>-u’/1-u²</p>
8
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d/dx[arcsec(u)]

u’/[|u|sqrt(1-u²)]

<p>u’/[|u|sqrt(1-u²)]</p>
9
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d/dx[arccsc(u)]

u’/[|u|sqrt(1-u²)]-

<p>u’/[|u|sqrt(1-u²)]-</p>
10
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y’’

d²y/d²x

<p>d²y/d²x</p>