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Popular >

derivative of sqrt(1+cos(2x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=\sqrt[5]{x^4}derivative of

implicit ln(xy^9)=xy implicit derivative

ln (x y^{9}) = x y

integral of (x^3)/(27)-4/9 x^2+4/3 x+1

\int \frac{x ^{3}}{27} - \frac{4}{9} x^{2} + \frac{4}{3} x + 1 d x

derivative of-3/(sqrt(x^5))

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

xy^'+y=(xy)^{3/2}

x y^{^{'}} + y = (x y)^{\frac{3}{2}}

Frequently Asked Questions (FAQ)

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