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Popular >

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

Solution

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

Solution

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

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

Simplify

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

= - 2 x tan (x^{2} + 1)

Popular Examples

derivative of f(v)=e^{2sin(3v)}derivative of

f (v) = e^{2 s i n (3 v)}

integral of sin(x)-cos(x)

\int sin (x) - cos (x) d x

sum from n=1 to infinity of (-3)^n

n = 1 \sum \infty (- 3)^{n}

(dy)/(dx)=(x-3)/(y+5)

\frac{d y}{d x} = \frac{x - 3}{y + 5}

sum from n=1 to infinity of 3*(1/5)^n

n = 1 \sum \infty 3 \cdot (\frac{1}{5})^{n}

Frequently Asked Questions (FAQ)

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