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)

d er i v a t i v e ln (x^{2} + x)

d er i v a t i v e 42 x^{\frac{1}{2}}

d er i v a t i v e \frac{1}{r}

d er i v a t i v e 1 + x tan (x)

d er i v a t i v e 3 x^{2} - 5 x^{3} + 4 x^{20}

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)