What is the derivative of 7x^2ln(x) ?

The derivative of 7x^2ln(x) is 7(2xln(x)+x)

What is the first derivative of 7x^2ln(x) ?

The first derivative of 7x^2ln(x) is 7(2xln(x)+x)

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\frac{d}{d x} (7 x^{2} ln (x))

7 (2 x ln (x) + x)

Solution steps

\frac{d}{d x} (7 x^{2} ln (x))

Take the constant out:

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

= 7 \frac{d}{d x} (x^{2} ln (x))

Apply the Product Rule:

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

f = x^{2}, g = ln (x)

= 7 (\frac{d}{d x} (x^{2}) ln (x) + \frac{d}{d x} (ln (x)) x^{2})

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

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

= 7 (2 x ln (x) + \frac{1}{x} x^{2})

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

= 7 (2 x ln (x) + x)

What is the derivative of 7x^2ln(x) ?
The derivative of 7x^2ln(x) is 7(2xln(x)+x)
What is the first derivative of 7x^2ln(x) ?
The first derivative of 7x^2ln(x) is 7(2xln(x)+x)