What is the derivative of x^3ln(4x) ?

The derivative of x^3ln(4x) is 3x^2ln(4x)+x^2

What is the first derivative of x^3ln(4x) ?

The first derivative of x^3ln(4x) is 3x^2ln(4x)+x^2

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derivative of

x^{3} ln (4 x)

3 x^{2} ln (4 x) + x^{2}

Solution steps

\frac{d}{d x} (x^{3} ln (4 x))

Apply the Product Rule:

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

f = x^{3}, g = ln (4 x)

= \frac{d}{d x} (x^{3}) ln (4 x) + \frac{d}{d x} (ln (4 x)) x^{3}

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

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

= 3 x^{2} ln (4 x) + \frac{1}{x} x^{3}

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

= 3 x^{2} ln (4 x) + x^{2}

\int e^{7 x} cos (2 x) d x

x \to 2 + lim (2 - x)

\int sin^{6} (x) cos (x) d x

\int (3 y) d y

x^{n}

What is the derivative of x^3ln(4x) ?
The derivative of x^3ln(4x) is 3x^2ln(4x)+x^2
What is the first derivative of x^3ln(4x) ?
The first derivative of x^3ln(4x) is 3x^2ln(4x)+x^2