What is the derivative of f(x)=3x^3(x^2-2) ?

The derivative of f(x)=3x^3(x^2-2) is 3(5x^4-6x^2)

What is the first derivative of f(x)=3x^3(x^2-2) ?

The first derivative of f(x)=3x^3(x^2-2) is 3(5x^4-6x^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = x^{2} - 2

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

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

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

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

Simplify

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

= 3 (5 x^{4} - 6 x^{2})

f (x) = (3 x^{2} - 2) (5 x + 5)

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

y = 5 x - x^{2}, y = - x

\frac{\partial}{\partial x} (3 y cos (x))

What is the derivative of f(x)=3x^3(x^2-2) ?
The derivative of f(x)=3x^3(x^2-2) is 3(5x^4-6x^2)
What is the first derivative of f(x)=3x^3(x^2-2) ?
The first derivative of f(x)=3x^3(x^2-2) is 3(5x^4-6x^2)