What is the derivative of 6x(x^2-1^2) ?

The derivative of 6x(x^2-1^2) is 6(5x^4-6x^2+1)

What is the first derivative of 6x(x^2-1^2) ?

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

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\frac{d}{d x} (6 x (x^{2} - 1)^{2})

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

Solution steps

\frac{d}{d x} (6 x (x^{2} - 1)^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \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}

= 6 (\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)

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

Simplify

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

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

\int_{0}^{1} \frac{1}{16 - x ^{2}} d x

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

y d x + x^{2} + 1 d y = 0

\int x x - 18 d x

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

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