Usage of product and chain rule
Given term: f ( x ) = ( 2 x − 3 ) ( 8 − x ) 2 Evaluate f ′ ( x )
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1 solution
- Using both the product and chain rule, we get: f ′ ( x ) = 2 ( 8 − x ) 2 + ( 2 x − 3 ) ( ( 2 ( 8 − x ) ( − 1 ) )
- Simplify using the binomial formula: f ′ ( x ) = 2 ( 6 4 − 1 6 x + x 2 ) + ( 2 x − 3 ) ( ( 2 ( 8 − x ) ( − 1 ) )
- The rest is a simplification of an algebraic expression: f ′ ( x ) = 6 x 2 − 7 0 x + 1 7 6