Find dy dx where y = 2sin. Basic Properties and Formulas If fx and g x are differentiable functions (the derivative exists), c and n are any real numbers, 1. cf cf x 2. fg fx gx 3. fg f g fg – Product Rule 4. 27x2+ 6x. We say that the number mo is the derivative offat xo, pro vided that: 1. Quotient Rule: f g 0 = f0g 0fg g2 5. 9x3+3x2+1. • ′ =× ′( ) • The derivative of a function multiplied by a constant is the constant multiplied by the derivative. • The derivative of the sum of two functions is the sums of their individual derivatives. Power Rule: d dx (xn) = nxn 1 3. • (c)’=0 Constant Rule: d dx (c) = 0; where c is a constant 2. Derivatives Cheat Sheet Derivative Rules 1. œ- Ð Ð-0Ñœ-0ww the “prime notion” in the other formulas as well) multiple Derivative of sum or () ..?. du dx Chain-Cosine Rule Ex2a. Derivative of constan ..?t ( ) We could also write , and could use.B .B-? lnx 1 dx d − … Answer: 2. Higher Derivatives 1. m m n n n x m(m 1)....(m n 1)x dx d = − − + − 2. @ () n n 1 n n x n 1 ! Definition Let f be a function whose domain contains an open interval about xo. () − − − × × × × − = − 2 1 n n n 1 n n x 2 1 3 5 .... 2n 3 x 1 dx d 3. n 1 n n n x n! 2. 1 x 1 dx d + = − 4. x x n n e e dx d = 5. ax b n ax b n n e a e dx d + = + 6. x x ()n n n a a lna dx d = 7. Product Rule: (fg)0 = f0g +fg0 4. For every m

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