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

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

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

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

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

- \frac{x}{2 4 - x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{2 2 ^{2} - x ^{2}} \frac{d}{d x} (2^{2} - x^{2})

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

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

= \frac{1}{2} \cdot \frac{1}{2 2 ^{2} - x ^{2}} (- 2 x)

Simplify

\frac{1}{2} \cdot \frac{1}{2 2 ^{2} - x ^{2}} (- 2 x) : - \frac{x}{2 4 - x ^{2}}

= - \frac{x}{2 4 - x ^{2}}

7 x^{2} - x^{3}

(x - 2) (4 x + 2)

4^{s i n^{2} (x) + c o s (3 x)}

(\frac{1}{t})^{^{'}}

(e^{\frac{x}{2}})^{^{'}}

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