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Popular Calculus >

derivative of f(x)=(x^2+3)(x^2-3)x^2

Solution

derivative of

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

Solution

6 x^{5} - 18 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x^{2} - 3) x^{2}) = 4 x^{3} - 6 x

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

Simplify

2 x (x^{2} - 3) x^{2} + (4 x^{3} - 6 x) (x^{2} + 3) : 6 x^{5} - 18 x

= 6 x^{5} - 18 x

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2+3)(x^2-3)x^2 ?
The derivative of f(x)=(x^2+3)(x^2-3)x^2 is 6x^5-18x
What is the first derivative of f(x)=(x^2+3)(x^2-3)x^2 ?
The first derivative of f(x)=(x^2+3)(x^2-3)x^2 is 6x^5-18x