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

The derivative of (ln(x^5)^2) is (50ln(x))/x

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

The first derivative of (ln(x^5)^2) is (50ln(x))/x

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

\frac{50 ln ( x )}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 ln (x^{5}) \frac{5}{x} : \frac{50 ln ( x )}{x}

= \frac{50 ln ( x )}{x}

f (x) = \frac{20}{3} x^{3} + 380 x^{2}

\frac{\partial}{\partial x} (3 ln (x) + ln (y))

\frac{\partial}{\partial x} (400 e^{x y})

n = 1 \sum \infty n sin (n)

n = 1 \sum \infty \frac{5}{3 ^{2 n}}

What is the derivative of (ln(x^5)^2) ?
The derivative of (ln(x^5)^2) is (50ln(x))/x
What is the first derivative of (ln(x^5)^2) ?
The first derivative of (ln(x^5)^2) is (50ln(x))/x