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# MS2 POwer Rules

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### MS2 POwer Rules

1. 1. d1. dx ( c ) = 0 ( c is a constant ) Ex f ( x) = 5 . f ′( x) = 02. d n dx ( ) x = nx n −1 ( n is a real number ) Ex f ( x) = x 7 . f ′( x) = 7 x 6
2. 2. d d3. dx ( cf ( x) ) = c dx ( f ( x) ) ( c is a constant ) 8 Ex f ( x) = 3 x ( ) . f ′( x) = 3 8 x 7 = 24 x 7 d d d4. dx  f ( x ) ± g ( x )  = dx [ f ( x)] ± dx [ g ( x) ]   Ex f ( x) = 7 + x12 . f ′( x) = 0 + 12 x11 = 12 x11
3. 3. f ( x) = 5x3 − 2 x 2 + 7 x + 4
4. 4. f ( x ) = 3 x 2 − 4 x −3 + 1
5. 5. f ( x) = 6x2 + 6x = −2
6. 6. y = 4 x3 + 2 x dyf ( x) = dx d2yf "( x) = 2 dx
7. 7. 4f ( x ) = 10 x − 2 + 2 x
8. 8. f ( x) = 6 x 2 − 5x + 2f ( x ) = 4 x 3 + 10 x − 7 2 3 9 2f ( x) = x + x + 3 3 2 3f ( x ) = −3 x + 5 x − 3x + 7 4 2 5
9. 9. f ( x ) = 2 x + 3x + 1 3 1 6 2f ( x) = x + − 2 3 x 4 2f ( x) = 2 + x x 5f ( x ) = 100 − 6 x − 3x 4
10. 10. f ( x) = x7 + x5y = x2 + 4x + 3D( t ) = 40t − 10t 2y = 4x +1
11. 11. f ( x ) = 3x 3 + 2 xf ( x) = x 4 + x3 3H ( x ) = 2 + 3x 2 xg ( x) = x + x −1 −2