Basic Differentian Rules *with u and v

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26 Terms

1
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D/dx {u±v}

d/dx u +d/dx v

2
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d/dx c

0

3
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d/x cu

c (u’)

4
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d/dx (x)

1

5
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d/dx (un)

nun-1(u’)

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d/dx (uv)

u(v’)+v(u’)

7
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d/dx [f(g(x))]

f’(g(x)) times g’(x)

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d/dx lnu

1/u (u’)

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d/dx [logau]

1/u(lna) times u’

10
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eu

eu (u’)

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d/dx au

au (lna (u’))

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sinu

cosu (u’)

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cosu

-sinu (u’)

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secu

secutanu (u’)

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cscu

-cscucotu (u’)

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tanu

sec2u (u’)

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cotu

-csc2u(u’)

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arcsinu

1/√ of (1-u2) * u’

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arccosu

-1/√(1-u2) *(u’)

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arcsecu

1/ |u| √(u2-1) * u’

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d/dx arccsc

-1 / (|u|√(u² - 1)) * (du/dx)

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d/dx arctanu

1/ 1+u2 (u’)

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arccotu

-1/(1+u2) (u’)

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d/x [f-1(x)]

1/f’(f-1(x)

25
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dy/dx when in parametric

(dy/dt)/(dx/dt)

26
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d2y/dx2 when in parametric

(d/dt(dy/dx)) / (dx/dt)