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

The derivative of f(x)=2x^3ln(x) is 2(3x^2ln(x)+x^2)

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

The first derivative of f(x)=2x^3ln(x) is 2(3x^2ln(x)+x^2)

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derivative of

f (x) = 2 x^{3} ln (x)

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = ln (x)

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

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

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

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

\frac{1}{x} x^{3} = x^{2}

= 2 (3 x^{2} ln (x) + x^{2})

What is the derivative of f(x)=2x^3ln(x) ?
The derivative of f(x)=2x^3ln(x) is 2(3x^2ln(x)+x^2)
What is the first derivative of f(x)=2x^3ln(x) ?
The first derivative of f(x)=2x^3ln(x) is 2(3x^2ln(x)+x^2)