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Popular >

derivative of sin^{1/2}(x)

Solution

\frac{d}{d x} (sin^{\frac{1}{2}} (x))

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of 10x+9x^2+3y

\frac{d}{d x} (10 x + 9 x^{2} + 3 y)

implicit (dy)/(dx),y=arcsin(2x+1)implicit derivative

\frac{d y}{d x}, y = arcsin (2 x + 1)

taylor e^{(t^2)/2}taylor

e^{\frac{t ^{2}}{2}}

(\partial)/(\partial x)(((xy^2))/(x^2+y^2))

\frac{\partial}{\partial x} (\frac{( x y ^{2} )}{x ^{2} + y ^{2}})

integral of (csc^2(2x))/(4-cot(2x))

\int \frac{csc ^{2} ( 2 x )}{4 - cot ( 2 x )} d x

Frequently Asked Questions (FAQ)

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