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

The derivative of 4x(x^2-2^2) is 4(5x^4-12x^2+4)

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

The first derivative of 4x(x^2-2^2) is 4(5x^4-12x^2+4)

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

4 (5 x^{4} - 12 x^{2} + 4)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 (1 \cdot (x^{2} - 2)^{2} + 4 x (x^{2} - 2) x) : 4 (5 x^{4} - 12 x^{2} + 4)

= 4 (5 x^{4} - 12 x^{2} + 4)

f (x) = e^{x} - 1

f (x) = x^{3} - 4

\int (1 - x - y)^{2} d y

\int \frac{1}{4 y} d y

\int cos^{4} (5 x) sin (5 x) d x

What is the derivative of 4x(x^2-2^2) ?
The derivative of 4x(x^2-2^2) is 4(5x^4-12x^2+4)
What is the first derivative of 4x(x^2-2^2) ?
The first derivative of 4x(x^2-2^2) is 4(5x^4-12x^2+4)