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Popular Calculus >

((3x^2+3x+4)^'(3x^2+6x)^')^'

Solution

((3 x^{2} + 3 x + 4)^{^{'}} (3 x^{2} + 6 x)^{^{'}})^{^{'}}

Solution

72 x + 54

Solution steps

((3 x^{2} + 3 x + 4)^{'} (3 x^{2} + 6 x)^{'})^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (3 x^{2} + 3 x + 4)^{'}, g = (3 x^{2} + 6 x)^{'}

= (3 x^{2} + 3 x + 4)^{^{''}} (3 x^{2} + 6 x)^{^{'}} + (3 x^{2} + 6 x)^{^{''}} (3 x^{2} + 3 x + 4)^{^{'}}

(3 x^{2} + 3 x + 4)^{''} = 6

(3 x^{2} + 6 x)^{'} = 6 x + 6

(3 x^{2} + 6 x)^{''} = 6

(3 x^{2} + 3 x + 4)^{'} = 6 x + 3

= 6 (6 x + 6) + 6 (6 x + 3)

Simplify

6 (6 x + 6) + 6 (6 x + 3) : 72 x + 54

= 72 x + 54

Graph

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Frequently Asked Questions (FAQ)

What is the ((3x^2+3x+4)^'(3x^2+6x)^')^' ?
The ((3x^2+3x+4)^'(3x^2+6x)^')^' is 72x+54
What is the first ((3x^2+3x+4)^'(3x^2+6x)^')^' ?
The first ((3x^2+3x+4)^'(3x^2+6x)^')^' is 72x+54