Derivative Rules MATH 142
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This 3 page Class Notes was uploaded by Abbey McCoy on Sunday January 24, 2016. The Class Notes belongs to MATH 142 at University of South Carolina taught by Dr. Zeimke in Spring 2016. Since its upload, it has received 40 views. For similar materials see Calculus II in Applied Mathematics at University of South Carolina.
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Date Created: 01/24/16
Derivative Rules d (c)=0 dx d (x)=1 dx d n n−1 dx (x )=nx d c• f(x )=c• f '(x) dx ( ) d (f (x)±g (x )= f'(x)±g '(x) dx d ' ' Product Rule: (f(x)•g (x))= f (x)g(x + f (x)g (x) dx d f x ) g x )f'(x)− f x )g'x ) Quotient Rule: ( ) = 2 dx g x ) |g x | d Chain Rule: (f(g (x))= f ( x ))g 'x ) dx d x x dx (e )=e d (ax)=a ln a ) dx d 1 (ln(x)) dx x x 1 loga¿= xln( ) d ¿ dx g( ) If you have a function |f(x | , use Logarithmic Differentiation. d (sin(x))cos (x) dx d dx (cos(x )=−sin (x) d 2 dx (tan(x))=sec (x) d (csc(x))=−csc (x)cot(x) dx d (ec(x )sec x tan(x) dx d (ot(x))−csc 2(x) dx d −1 1 dx (in (x)= 2 √1−x d −1 −1 dx (os (x)) 2 √ 1−x d −1 1 dx (an (x)) 1+x 2 d −1 −1 dx (sc (x)) x x −1 √ d −1 1 dx (ec (x)) x x −1 √ d cot−1(x)= −1 dx ( ) 1+x 2
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