en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

\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}

Popular Examples

derivative of f(x)= 20/3 x^3+380x^2 derivative of

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

(\partial)/(\partial x)(3ln(x)+ln(y))

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

(\partial)/(\partial x)(400e^{xy})

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

sum from n=1 to infinity of nsin(n)

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

sum from n=1 to infinity of 5/(3^{2n)}

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

Frequently Asked Questions (FAQ)

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