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Popular >

derivative of sqrt(cos(x+1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(d^2)/(dx^2)(5ln(x^5))

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

integral of ((2x^3+5x^2-2x)/x)

\int (\frac{2 x ^{3} + 5 x ^{2} - 2 x}{x}) d x

area sin(x),cos(x)-1 area

sin (x), cos (x) - 1

integral from 1 to 5 of x^3-10x^2+29x-20

\int_{1}^{5} x^{3} - 10 x^{2} + 29 x - 20 d x

(\partial)/(\partial y)(2x-1)

\frac{\partial}{\partial y} (2 x - 1)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(cos(x+1)) ?
The derivative of sqrt(cos(x+1)) is -(sin(x))/(2sqrt(cos(x)+1))
What is the first derivative of sqrt(cos(x+1)) ?
The first derivative of sqrt(cos(x+1)) is -(sin(x))/(2sqrt(cos(x)+1))