What is the derivative of cos^4(x/2)-sin^4(x/2) ?

The derivative of cos^4(x/2)-sin^4(x/2) is -sin(x)

What is the first derivative of cos^4(x/2)-sin^4(x/2) ?

The first derivative of cos^4(x/2)-sin^4(x/2) is -sin(x)

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derivative of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2})

- sin (x)

Solution steps

\frac{d}{d x} (cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (cos^{4} (\frac{x}{2})) - \frac{d}{d x} (sin^{4} (\frac{x}{2}))

\frac{d}{d x} (cos^{4} (\frac{x}{2})) = - 2 cos^{3} (\frac{x}{2}) sin (\frac{x}{2})

\frac{d}{d x} (sin^{4} (\frac{x}{2})) = 2 sin^{3} (\frac{x}{2}) cos (\frac{x}{2})

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

Simplify

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

= - sin (x)

\frac{- x ^{3} + x - 1}{2}

y = (x^{3} - x) e^{- 3} x

z (3 x)^{4}

\frac{x}{10}

lo g_{10} (3 x + 2016)

What is the derivative of cos^4(x/2)-sin^4(x/2) ?
The derivative of cos^4(x/2)-sin^4(x/2) is -sin(x)
What is the first derivative of cos^4(x/2)-sin^4(x/2) ?
The first derivative of cos^4(x/2)-sin^4(x/2) is -sin(x)