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

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

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

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

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

- cos (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - cos (x)

cos (x), sin (x), 0, \frac{π}{2}

\frac{d y}{d x} = 10 y \cdot e^{x + 7}

\int (x + 1) 3 x + 2 d x

\int \frac{1}{- y ^{2}} d y

n = 1 \sum \infty (\frac{6}{7})^{n}

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