What is the derivative of (4x-2)^3(x^2+1)^2 ?

The derivative of (4x-2)^3(x^2+1)^2 is 12(4x-2)^2(x^2+1)^2+4x(x^2+1)(4x-2)^3

What is the first derivative of (4x-2)^3(x^2+1)^2 ?

The first derivative of (4x-2)^3(x^2+1)^2 is 12(4x-2)^2(x^2+1)^2+4x(x^2+1)(4x-2)^3

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derivative of

(4 x - 2)^{3} (x^{2} + 1)^{2}

12 (4 x - 2)^{2} (x^{2} + 1)^{2} + 4 x (x^{2} + 1) (4 x - 2)^{3}

Solution steps

\frac{d}{d x} ((4 x - 2)^{3} (x^{2} + 1)^{2})

Apply the Product Rule:

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

f = (4 x - 2)^{3}, g = (x^{2} + 1)^{2}

= \frac{d}{d x} ((4 x - 2)^{3}) (x^{2} + 1)^{2} + \frac{d}{d x} ((x^{2} + 1)^{2}) (4 x - 2)^{3}

\frac{d}{d x} ((4 x - 2)^{3}) = 12 (4 x - 2)^{2}

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= 12 (4 x - 2)^{2} (x^{2} + 1)^{2} + 4 x (x^{2} + 1) (4 x - 2)^{3}

What is the derivative of (4x-2)^3(x^2+1)^2 ?
The derivative of (4x-2)^3(x^2+1)^2 is 12(4x-2)^2(x^2+1)^2+4x(x^2+1)(4x-2)^3
What is the first derivative of (4x-2)^3(x^2+1)^2 ?
The first derivative of (4x-2)^3(x^2+1)^2 is 12(4x-2)^2(x^2+1)^2+4x(x^2+1)(4x-2)^3