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Popular >

derivative of x(ln(5x)^2)

Solution

\frac{d}{d x} (x (ln (5 x))^{2})

Solution

ln^{2} (5 x) + 2 ln (5 x)

Solution steps

\frac{d}{d x} (x (ln (5 x))^{2})

Apply the Product Rule:

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

f = x, g = (ln (5 x))^{2}

= \frac{d x}{d x} (ln (5 x))^{2} + \frac{d}{d x} ((ln (5 x))^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((ln (5 x))^{2}) = \frac{2 ln ( 5 x )}{x}

= 1 \cdot (ln (5 x))^{2} + \frac{2 ln ( 5 x )}{x} x

Simplify

1 \cdot ln^{2} (5 x) + \frac{2 ln ( 5 x )}{x} x : ln^{2} (5 x) + 2 ln (5 x)

= ln^{2} (5 x) + 2 ln (5 x)

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y^{^{'}} - 3 y = e^{3 x} 4 - x^{2}

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x \to - 2 - lim (x + 1)

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x \to 0 lim (\frac{1}{sin ( 2 x )})

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x \to 3 π lim (x^{3} sin^{4} (x))

Frequently Asked Questions (FAQ)

What is the derivative of x(ln(5x)^2) ?
The derivative of x(ln(5x)^2) is ln^2(5x)+2ln(5x)
What is the first derivative of x(ln(5x)^2) ?
The first derivative of x(ln(5x)^2) is ln^2(5x)+2ln(5x)