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

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

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

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

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derivative of

sin^{4} (\frac{x}{4}) + cos^{4} (\frac{x}{4})

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x y + y + 2 x + 2)

f (θ) = θ cos (θ) sin (θ)

\frac{\partial}{\partial y} (y^{2} - 4 y + x y)

\int (4 x^{2} - 9 x)^{5} (8 x - 9) d x

x \to 0 lim (\frac{sin ^{3} ( x )}{x ^{2}})

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