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

The derivative of x^3(4-x) is 12x^2-4x^3

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

The first derivative of x^3(4-x) is 12x^2-4x^3

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

12 x^{2} - 4 x^{3}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = 4 - x

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

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

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

= 3 x^{2} (4 - x) + (- 1) x^{3}

Simplify

3 x^{2} (4 - x) + (- 1) x^{3} : 12 x^{2} - 4 x^{3}

= 12 x^{2} - 4 x^{3}

n = 0 \sum \infty \frac{4}{n ( n + 2 )}

n = 0 \sum \infty \frac{( 5 ^{n} )}{n !}

tan^{2} (θ)

\int \frac{w ^{2}}{( w ^{2} + 7 ) ^{2}} d w

y^{^{'}} = - \frac{2 x}{y}, y (1) = 10

What is the derivative of x^3(4-x) ?
The derivative of x^3(4-x) is 12x^2-4x^3
What is the first derivative of x^3(4-x) ?
The first derivative of x^3(4-x) is 12x^2-4x^3