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

The derivative of sqrt(1+cos^2(x)) is -(sin(2x))/(2sqrt(1+cos^2(x)))

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

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

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

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

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

Simplify

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

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

\int (x - 2) e^{x} d x

y = 2 arcsin (3) x^{5}

y = 5 - 7 x^{2}, (3, - 58)

\int \frac{5 sin ( x )}{cos ^{3} ( x )} d x

\int \frac{x ^{2}}{2} d x

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