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derivative of 4x(4x-2(x^2-3))

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ddx (4x(4x−2)(x²−3))

Solution

4(16x³−6x²−24x+6)

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ddx (4x(4x−2)(x²−3))

Take the constant out: (a·f)′=a·f ′

=4ddx (x(4x−2)(x²−3))

Apply the Product Rule: (f·g)′=f ′·g+f·g′

f=x, g=(4x−2)(x²−3)

=4(dxdx (4x−2)(x²−3)+ddx ((4x−2)(x²−3))x)

dxdx =1

ddx ((4x−2)(x²−3))=12x²−4x−12

=4(1· (4x−2)(x²−3)+(12x²−4x−12)x)

Simplify 4(1· (4x−2)(x²−3)+(12x²−4x−12)x): 4(16x³−6x²−24x+6)

=4(16x³−6x²−24x+6)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

derivative of 4x(4x-2(x^2-3))

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