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

The derivative of (x+2(3x^2-4)^2) is 45x^4+72x^3-72x^2-96x+16

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

The first derivative of (x+2(3x^2-4)^2) is 45x^4+72x^3-72x^2-96x+16

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

45 x^{4} + 72 x^{3} - 72 x^{2} - 96 x + 16

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (3 x^{2} - 4)^{2} + 12 x (3 x^{2} - 4) (x + 2) : 45 x^{4} + 72 x^{3} - 72 x^{2} - 96 x + 16

= 45 x^{4} + 72 x^{3} - 72 x^{2} - 96 x + 16

What is the derivative of (x+2(3x^2-4)^2) ?
The derivative of (x+2(3x^2-4)^2) is 45x^4+72x^3-72x^2-96x+16
What is the first derivative of (x+2(3x^2-4)^2) ?
The first derivative of (x+2(3x^2-4)^2) is 45x^4+72x^3-72x^2-96x+16