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Derivative

Derivative

Derivative

f ( x ) = x 6 3 − 2 x d d x [ x 6 3 − 2 x ] = d d x [ x 6 ] 3 − 2 ⋅ d d x [ x ] = 6 x 5 3 − 2 ⋅ 1 = 2 x 5 − 2 f ( x ) = ( x 3 − 2 x ) ⋅ ( x 5 + 6 x 2 ) d d x [ ( x 3 − 2 x ) ⋅ ( x 5 + 6 x 2 ) ] aaaa = d d x [ x 3 − 2 x ] ⋅ ( x 5 + 6 x 2 ) + ( x 3 − 2 x ) ⋅ d d x [ x 5 + 6 x 2 ] = ( d d x [ x 3 ] − 2 ⋅ d d x [ x ] ) ⋅ ( x 5 + 6 x 2 ) + ( d d x [ x 5 ] + 6 ⋅ d d x [ x 2 ] ) ⋅ ( x 3 − 2 x ) = ( 3 x 2 − 2 ⋅ 1 ) ⋅ ( x 5 + 6 x 2 ) + ( 5 x 4 + 6 ⋅ 2 x ) ⋅ ( x 3 − 2 x ) = ( 3 x 2 − 2 ) ⋅ ( x 5 + 6 x 2 ) + ( x 3 − 2 x ) ⋅ ( 5 x 4 + 12 x ) Rewrite/simplify: = 8 x 7 − 12 x 5 + 30 x 4 − 36 x 2