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Popular >

derivative of-cos(sqrt(x))

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches-1 of-x^2+2x-9

x \to - 1 lim (- x^{2} + 2 x - 9)

-y^'+(4y)/x =xy^2

- y^{^{'}} + \frac{4 y}{x} = x y^{2}

integral of (x^2)/((x^3+1)^5)

\int \frac{x ^{2}}{( x ^{3} + 1 ) ^{5}} d x

inverse oflaplace s/(s^2+4s+3)inverse laplace

\frac{s}{s ^{2} + 4 s + 3}

(\partial)/(\partial x)(4x^{0.75}+y)

\frac{\partial}{\partial x} (4 x^{0.75} + y)

Frequently Asked Questions (FAQ)

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