What is the derivative of (cos(x^3))/2 ?

The derivative of (cos(x^3))/2 is -(3x^2sin(x^3))/2

What is the first derivative of (cos(x^3))/2 ?

The first derivative of (cos(x^3))/2 is -(3x^2sin(x^3))/2

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derivative of

\frac{cos ( x ^{3} )}{2}

- \frac{3 x ^{2} sin ( x ^{3} )}{2}

Solution steps

\frac{d}{d x} (\frac{cos ( x ^{3} )}{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (cos (x^{3}))

Apply the chain rule:

- sin (x^{3}) \frac{d}{d x} (x^{3})

= - sin (x^{3}) \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{2} (- sin (x^{3}) \cdot 3 x^{2})

Simplify

\frac{1}{2} (- sin (x^{3}) \cdot 3 x^{2}) : - \frac{3 x ^{2} sin ( x ^{3} )}{2}

= - \frac{3 x ^{2} sin ( x ^{3} )}{2}

What is the derivative of (cos(x^3))/2 ?
The derivative of (cos(x^3))/2 is -(3x^2sin(x^3))/2
What is the first derivative of (cos(x^3))/2 ?
The first derivative of (cos(x^3))/2 is -(3x^2sin(x^3))/2