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Popular >

derivative of ln(-cos(x^2+1))

Solution

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

Solution

\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}

Popular Examples

derivative of sin(x/(sqrt(x+1)))

\frac{d}{d x} (sin (\frac{x}{x + 1}))

limit as x approaches 7 of (x-7)^2+x^2

x \to 7 lim ((x - 7)^{2} + x^{2})

limit as x approaches 0+of ln(1/(x^4))

x \to 0 + lim (ln (\frac{1}{x ^{4}}))

derivative of u(x)=sqrt(x)derivative of

u (x) = x

derivative of f(x)=3x^3+15x^2+29x+3 derivative of

f (x) = 3 x^{3} + 15 x^{2} + 29 x + 3

Frequently Asked Questions (FAQ)

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)