Advanced Calculus Differentiation and Evaluation Techniques
Explore various differentiation and evaluation problems in calculus, including straight line forms, chain rules, simplification, and more. Enhance your understanding of calculus concepts with these detailed examples and solutions.
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Presentation Transcript
Differentiation Evaluation 2 4 3 7 x x + Differentiate x 8 3
Differentiation Evaluation = + + 3 2 2 7 4 4 y x x x Differentiate = + 2 6 14 4 y x x
Differentiation Evaluation 16 3 = 2 ( ) A x 240 x x Differentiate 32 3 = ( ) A x 240 x
Calculus Evaluation 800 r 3 r 2 Differentiate 2 1 3 800 r r Straight line form ( 1)800 2 6 r r Differentiate
Calculus Evaluation 43200 x = + 2 ( ) A x x Differentiate x = + 2 1 ( ) A x 43200 x Straight line form ( ) x = 2 2 43200 A x x Chain Rule 43200 x ( ) = 2 A x x Simplify 2
Calculus Evaluation + (3 5)( 2) x x Differentiate + 2 + 3 10 x x 2 3 6 5 10 x x x Multiply out x+ 6 1 Differentiate
Calculus Evaluation 2 ( 2 ) x x x Differentiate 3 2 2 x x multiply out 2 3 4 x x differentiate
Calculus Evaluation ( x x x ) 2 Differentiate 1 ( ) 2 2x x x Straight line form 5 2 3 2 x x multiply out 3 2 1 2 5 2 3 2 x x Differentiate
Calculus Evaluation 3 4 = (8 ) A a a Differentiate 3 4 = 2 6 A a a multiply out 3 2 = 6 A a Differentiate
Calculus Evaluation ( 2 4 x )( ) x Differentiate + 4 8 2 x x x multiply out 6 8 x x Simplify 1 2 6 8 x x Straight line form 1 2 Differentiate 3 1 x
Calculus Evaluation 3 3 2 16 x = + 2 ( ) A x x Differentiate 3 3 2 3 3 16 2 = + 2 ( ) A x x Multiply out x 3 3 2 x = + 2 1 ( ) A x 24 3 x Straight line form x = 2 ( ) A x 3 3 24 3 x Differentiate
Calculus Evaluation 3 2 6 3 x x x x + + 9 Differentiate 3 2 6 3 9 x x x x x x + + Split up x x + 3 9 + 2 1 6 x x Straight line form x 6 9 + 2 2 x Differentiate
