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

The derivative of f(x)=3x^4(x^2-4x) is 3(6x^5-20x^4)

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

The first derivative of f(x)=3x^4(x^2-4x) is 3(6x^5-20x^4)

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derivative of

f (x) = 3 x^{4} (x^{2} - 4 x)

3 (6 x^{5} - 20 x^{4})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = x^{2} - 4 x

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

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

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

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

Expand

4 x^{3} (x^{2} - 4 x) + (2 x - 4) x^{4} : 6 x^{5} - 20 x^{4}

= 3 (6 x^{5} - 20 x^{4})

x \to 3 lim (\frac{∣ 3 - x ∣}{3 - x})

\int \frac{x ^{2}}{x + 15} d x

\int_{1}^{3} (x^{2} + \frac{1}{4 x ^{2}}) d x

\int (- 4 x^{6} - 5 x^{5} - 2 x^{2} + 5 - e^{x}) d x

\int (x + 3) (x - 3) d x

What is the derivative of f(x)=3x^4(x^2-4x) ?
The derivative of f(x)=3x^4(x^2-4x) is 3(6x^5-20x^4)
What is the first derivative of f(x)=3x^4(x^2-4x) ?
The first derivative of f(x)=3x^4(x^2-4x) is 3(6x^5-20x^4)