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Popular >

derivative of y=sqrt(cos(x))

Solution

derivative of

y = cos (x)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

taylor ln((1+x)/(1-x))taylor

ln (\frac{1 + x}{1 - x})

derivative of log_{5}(sqrt(4x^2+5x-8))

\frac{d}{d x} (lo g_{5} (4 x^{2} + 5 x - 8))

(\partial)/(\partial x)(sqrt(xy+y/x))

\frac{\partial}{\partial x} (x y + \frac{y}{x})

integral of (cos^5(5x+1))/(sin^4(5x+1))

\int \frac{cos ^{5} ( 5 x + 1 )}{sin ^{4} ( 5 x + 1 )} d x

tangent of y=((x-1))/(x+1)tangent of

y = \frac{( x - 1 )}{x + 1}

Frequently Asked Questions (FAQ)

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