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

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

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

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

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\frac{d}{d x} (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

\int \frac{4 + x}{16 - x ^{2}} d x

\int \frac{1}{2 + x} d x

t^{2} y^{^{''}} + t y^{^{'}} + 25 y = 0

\frac{d y}{d x} = 3 x

x \to - 1 lim (- x^{2} + 1)

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