What is the derivative of f(x)=(x^23x)/6 ?

The derivative of f(x)=(x^23x)/6 is (3x^2)/2

What is the first derivative of f(x)=(x^23x)/6 ?

The first derivative of f(x)=(x^23x)/6 is (3x^2)/2

derivative of

f (x) = \frac{x ^{2} 3 x}{6}

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

Solution steps

\frac{d}{d x} (\frac{x ^{2} \cdot 3 x}{6})

Take the constant out:

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

= \frac{3}{6} \frac{d}{d x} (x^{2} x)

Apply the Product Rule:

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

f = x^{2}, g = x

= \frac{3}{6} (\frac{d}{d x} (x^{2}) x + \frac{d x}{d x} x^{2})

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

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

= \frac{3}{6} (2 xx + 1 \cdot x^{2})

Simplify

\frac{3}{6} (2 xx + 1 \cdot x^{2}) : \frac{3 x ^{2}}{2}

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

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What is the derivative of f(x)=(x^23x)/6 ?
The derivative of f(x)=(x^23x)/6 is (3x^2)/2
What is the first derivative of f(x)=(x^23x)/6 ?
The first derivative of f(x)=(x^23x)/6 is (3x^2)/2