What is the derivative of-1/2 sin^2(x) ?

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

What is the first derivative of-1/2 sin^2(x) ?

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

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

- sin (x) cos (x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - sin (x) cos (x)

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