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Popular >

derivative of x(x^2-1^2)

Solution

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

Solution

5 x^{4} - 6 x^{2} + 1

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot (x^{2} - 1)^{2} + 4 x (x^{2} - 1) x : 5 x^{4} - 6 x^{2} + 1

= 5 x^{4} - 6 x^{2} + 1

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y^{''}+25y=30sin(5t)

y^{^{''}} + 25 y = 30 sin (5 t)

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x \to 0 lim (x^{2})

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\frac{d}{d x} (ln (x + x^{2} - 12))

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3 e^{x}, 3 x e^{x^{2}}, 0, 1

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\int 3 t sin (t) cos (t) d t

Frequently Asked Questions (FAQ)

What is the derivative of x(x^2-1^2) ?
The derivative of x(x^2-1^2) is 5x^4-6x^2+1
What is the first derivative of x(x^2-1^2) ?
The first derivative of x(x^2-1^2) is 5x^4-6x^2+1