CALC BC- Derivatives
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Last updated 5:22 PM on 9/14/24
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18 Terms
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Average Rate of Change
Slope (f(b)-f(a))/(b-a)
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Instantaneous Rate of Change
as the limit approaches c, (f(x)-f©)/(f-c)
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Limit Definition of the Derivative
As the limit of h approaches 0, (f(x+h)-f(x))/h
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sin²x+cos²x
=1
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sin(x+y)
=sinxcosy+cosxsiny
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cos(x+y)
cosxcosy-sinxsiny
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Tangent Line of a graph of f at x=c
y-f©=f’©(x-c)
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A line normal (perpendicular) to the graph of f at x=c
y-f©=(-1/f’©)(x-c)
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Derivative of a Constant
0
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Power Rule—→ x^n=
nx^(n-1)
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Exponential Base e^x=
e^x
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Logarithmic base lnx=
1/x
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Derivative of sinx=
cosx
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Derivative of tanx
sec²x
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Derivative of secx
secxtanx
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Derivative of cosx
-sinx
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Derivative of cotx
-csc²x
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Derivative of cscx
-cscxcotx
