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))

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

\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}

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))