What is the derivative of (x^2(x+1))/3 ?

The derivative of (x^2(x+1))/3 is (3x^2+2x)/3

What is the first derivative of (x^2(x+1))/3 ?

The first derivative of (x^2(x+1))/3 is (3x^2+2x)/3

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derivative of

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

\frac{3 x ^{2} + 2 x}{3}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = x + 1

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

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

\frac{d}{d x} (x + 1) = 1

= \frac{1}{3} (2 x (x + 1) + 1 \cdot x^{2})

Simplify

\frac{1}{3} (2 x (x + 1) + 1 \cdot x^{2}) : \frac{3 x ^{2} + 2 x}{3}

= \frac{3 x ^{2} + 2 x}{3}

ln ((2 x + 1)^{2})

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

y = sin (x^{2} + 2)

\frac{sin ( 1 + x ^{2} )}{( 1 - x ^{2} )}

(2 x - 4)^{3}

What is the derivative of (x^2(x+1))/3 ?
The derivative of (x^2(x+1))/3 is (3x^2+2x)/3
What is the first derivative of (x^2(x+1))/3 ?
The first derivative of (x^2(x+1))/3 is (3x^2+2x)/3