Differentiation Flashcards

1
Q

What is the chain rule?

A

dy/dx = dy/du x du/dx

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2
Q

What is the quotient rule?

A

dy/dx =

      v^2
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3
Q

If y=e^x, dy/dx = ?

A

e^x

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4
Q

For y= e^2x…

A

Use the chain rule.

u=2x du/dx = 2

y=e^u dy/du = e^u

dy/dx = 2e^u = 2e^2x

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5
Q

If y=sinx, dy/dx = ?

A

cosx

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6
Q

If y=cosx, dy/dx = ?

A

-sinx

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7
Q

sinx&raquo_space; cosx&raquo_space; -sinx&raquo_space; ?&raquo_space; ?

A

sinx&raquo_space; cosx&raquo_space; -sinx&raquo_space; -cosx&raquo_space; sinx

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8
Q

If y=tanx, dy/dx = ?

A

y = sinx/cosx

Use quotient rule:

u= sinx        du/dx = cosx
v= cosx       dv/dx = -sinx

dy/dx= cos^2x + sin^2x = 1
——————- ———–
cos^2x cos^2x

=sec^2x

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9
Q

What is the product rule?

A

If y=uv

dy/dx = u(dv/dx) + v(du/dx)

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