What is the derivative of x^2*In(x) ?

The derivative of x^2*In(x) is 3nx^2I

What is the first derivative of x^2*In(x) ?

The first derivative of x^2*In(x) is 3nx^2I

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\frac{d}{d x} (x^{2} \cdot I n (x))

3 n x^{2} I

Solution steps

\frac{d}{d x} (x^{2} I n (x))

Simplify

x^{2} I n (x) : n x^{3} I

= \frac{d}{d x} (n x^{3} I)

Treat

n, I

as a constant

Take the constant out:

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

= n I \frac{d}{d x} (x^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= n I \cdot 3 x^{3 - 1}

Simplify

= 3 n x^{2} I

What is the derivative of x^2*In(x) ?
The derivative of x^2*In(x) is 3nx^2I
What is the first derivative of x^2*In(x) ?
The first derivative of x^2*In(x) is 3nx^2I