What is the derivative of ln(-cos(x^2+1)) ?

The derivative of ln(-cos(x^2+1)) is (2xsin(x^2))/(-cos(x^2)+1)

What is the first derivative of ln(-cos(x^2+1)) ?

The first derivative of ln(-cos(x^2+1)) is (2xsin(x^2))/(-cos(x^2)+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (- cos (x^{2}) + 1))

\frac{2 x sin ( x ^{2} )}{- cos ( x ^{2} ) + 1}

Solution steps

\frac{d}{d x} (ln (- cos (x^{2}) + 1))

Apply the chain rule:

\frac{1}{- cos ( x ^{2} ) + 1} \frac{d}{d x} (- cos (x^{2}) + 1)

= \frac{1}{- cos ( x ^{2} ) + 1} \frac{d}{d x} (- cos (x^{2}) + 1)

\frac{d}{d x} (- cos (x^{2}) + 1) = 2 x sin (x^{2})

= \frac{1}{- cos ( x ^{2} ) + 1} \cdot 2 x sin (x^{2})

Simplify

\frac{1}{- cos ( x ^{2} ) + 1} \cdot 2 x sin (x^{2}) : \frac{2 x sin ( x ^{2} )}{- cos ( x ^{2} ) + 1}

= \frac{2 x sin ( x ^{2} )}{- cos ( x ^{2} ) + 1}

What is the derivative of ln(-cos(x^2+1)) ?
The derivative of ln(-cos(x^2+1)) is (2xsin(x^2))/(-cos(x^2)+1)
What is the first derivative of ln(-cos(x^2+1)) ?
The first derivative of ln(-cos(x^2+1)) is (2xsin(x^2))/(-cos(x^2)+1)