What is the derivative of-(cos(x)/(sqrt(x))) ?

The derivative of-(cos(x)/(sqrt(x))) is -(-2xsin(x)-cos(x))/(2xsqrt(x))

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

The first derivative of-(cos(x)/(sqrt(x))) is -(-2xsin(x)-cos(x))/(2xsqrt(x))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{\frac{d}{d x} ( cos ( x ) ) x - \frac{d}{d x} ( x ) cos ( x )}{( x ) ^{2}}

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

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

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

Simplify

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

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

\int \frac{5 x ^{3}}{x ^{2} - 1} d x

y^{^{''}} + 3 y^{^{'}} + 2 y = (1 + e^{t})^{- 1}

4 x^{- 3}

x \to - 5 lim (∣ x ∣ - 5)

(1 - x)^{- 100}

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