What is the derivative of y=x^2ln(4x) ?

The derivative of y=x^2ln(4x) is 2xln(4x)+x

What is the first derivative of y=x^2ln(4x) ?

The first derivative of y=x^2ln(4x) is 2xln(4x)+x

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derivative of

y = x^{2} ln (4 x)

2 x ln (4 x) + x

Solution steps

\frac{d}{d x} (x^{2} ln (4 x))

Apply the Product Rule:

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

f = x^{2}, g = ln (4 x)

= \frac{d}{d x} (x^{2}) ln (4 x) + \frac{d}{d x} (ln (4 x)) x^{2}

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

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

= 2 x ln (4 x) + \frac{1}{x} x^{2}

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

= 2 x ln (4 x) + x

lo g_{10} (∣ 3 x ∣)

2^{3} x

y = x^{2} e^{2}

4 y^{2} - 6 y + 5

lo g_{10} (x^{2} + a^{2})

What is the derivative of y=x^2ln(4x) ?
The derivative of y=x^2ln(4x) is 2xln(4x)+x
What is the first derivative of y=x^2ln(4x) ?
The first derivative of y=x^2ln(4x) is 2xln(4x)+x