What is the derivative of-1/15 cos(15sqrt(x)) ?

The derivative of-1/15 cos(15sqrt(x)) is (sin(15sqrt(x)))/(2sqrt(x))

What is the first derivative of-1/15 cos(15sqrt(x)) ?

The first derivative of-1/15 cos(15sqrt(x)) is (sin(15sqrt(x)))/(2sqrt(x))

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\frac{d}{d x} (- \frac{1}{15} cos (15 x))

\frac{sin ( 15 x )}{2 x}

Solution steps

\frac{d}{d x} (- \frac{1}{15} cos (15 x))

Take the constant out:

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

= - \frac{1}{15} \frac{d}{d x} (cos (15 x))

Apply the chain rule:

- sin (15 x) \frac{d}{d x} (15 x)

= - sin (15 x) \frac{d}{d x} (15 x)

\frac{d}{d x} (15 x) = \frac{15}{2 x}

= - \frac{1}{15} (- sin (15 x) \frac{15}{2 x})

Simplify

- \frac{1}{15} (- sin (15 x) \frac{15}{2 x}) : \frac{sin ( 15 x )}{2 x}

= \frac{sin ( 15 x )}{2 x}

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What is the derivative of-1/15 cos(15sqrt(x)) ?
The derivative of-1/15 cos(15sqrt(x)) is (sin(15sqrt(x)))/(2sqrt(x))
What is the first derivative of-1/15 cos(15sqrt(x)) ?
The first derivative of-1/15 cos(15sqrt(x)) is (sin(15sqrt(x)))/(2sqrt(x))