deriv1.pdf - Derivative Formulas In the following u and v...

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Derivative Formulas In the following, u and v are functions of x, and n , e , a , and k are constants. 1. 0 ( ) ( '( ) lim h ) f x h f x f x h + = The Definition of the Derivative. 2. ( ) 0 d k dx = The derivative of a constant is zero. 3. ( ) ( ) ( ) d d k u x k dx dx = u The derivative of a constant times a function. 4. ( ) 1 n n d d u nu dx dx = u The Power Rule (Variable raised to a constant). 5. ( ) d du u v dx dx dx + = + dv The Sum Rule. 6. ( ) d du u v dx dx dx = dv The Difference Rule. 7. ( ) ' d uv uv vu dx = + ' The Product Rule. 8. 2 ' ' d u vu uv dx v v = The Quotient Rule. 9. dy dy du dx du dx = The Chain Rule. 10. ( ) ( ) ( ( ( ) ' ( ) ' d ) f g x f g x g x dx = Another Form of the Chain Rule. 11. ( ) sin cos d u u dx dx = du The Derivative of the Sine. 12. ( ) cos sin d u u dx dx = − du The Derivative of the Cosine. 13. ( ) 2 tan sec d u u dx dx = du The Derivative of the Tangent.
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