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27 Cards in this Set
- Front
- Back
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sin(x) |
cos(x) |
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Cos(x) |
-Sin(x) |
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Tan(x) |
Sec^2(x) |
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Cot(x) |
-Csc^2(x) |
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Sec(x) |
Sec(x)Tan(x) |
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Csc(x) |
-Csc(x)Cot(x) |
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Definintion of Derivative |
(f(x-h)-f(x))/h |
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e^u |
E^u du |
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ln u |
1/u du |
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tangent line equation |
y-f(a)= f'(a)[x-a] |
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Inverse trig functions |
Evaluate Sin^-1(1/2) Sin(y)= 1/2 Unit circle see y=pi/6 |
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derivative Sin^-1(x) |
1/√(1-x^2) |
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derivative Cos^-1(x) |
-1/√(1-x^2) |
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derivative Tan^-1(x) |
1/(1+x^2) |
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derivative Cot^-1(x) |
-1/(1+x^2) |
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derivative Sec^-1(x) |
1/(|x|√(x^2-1)) |
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derivative of Csc^-1(x) |
-1/(|x|√(x^2-1)) |
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Growth and Decay Formula |
y(t)=y(0)e^(kt) |
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f^-1(a) |
f^1'(a)= 1/(f'(f^1(a))) |
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Related rates |
Draw picture, write down what is given, and write down what is wanted. |
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derivative of y=logbu |
u'/(u lna) |
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log (ab) log6x |
log a + log b log(6) + log(x) |
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ln y^x |
x ln y |
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ln(x/y) |
ln x- ln y |
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linear approximation |
L(x)=f'(a)[x-a]+f(a) |
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implicit differentiation |
x^2+y^2=12 find the derivative of both sides then solve for dy/dx |
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relation between f(x) and f^1(x) graphs |
the reflect across the line y=x |
