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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{1}{2}) = 0

= 2 (- sin (\frac{x}{2}) \frac{1}{2} - 0)

Simplify

2 (- sin (\frac{x}{2}) \frac{1}{2} - 0) : - sin (\frac{x}{2})

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

\int_{2}^{3} 4 e^{4 x} d x

y^{^{'}} + 3 y = t e^{4 t}

\int_{16}^{25} \frac{x - 16}{x} d x

\int cos (x) (8 + 5 sin^{2} (x)) d x

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