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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((2 x^{2} + 1)^{3}) = 12 x (2 x^{2} + 1)^{2}

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

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

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