What is the derivative of (4-x^2^{1/2}) ?

The derivative of (4-x^2^{1/2}) is -x/((4-x^2)^{1/2)}

What is the first derivative of (4-x^2^{1/2}) ?

The first derivative of (4-x^2^{1/2}) is -x/((4-x^2)^{1/2)}

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

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 ( 4 - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (4 - x^{2})

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

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

Simplify

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

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

\int_{0}^{\infty} 6 e^{- x} d x

n = 0 \sum \infty (x - 9)^{n}

\frac{d}{d x} (2 + ln (x))

y^{^{'}} + 4 x y = x

\frac{d}{d x} (ln (1 + x^{4}))

What is the derivative of (4-x^2^{1/2}) ?
The derivative of (4-x^2^{1/2}) is -x/((4-x^2)^{1/2)}
What is the first derivative of (4-x^2^{1/2}) ?
The first derivative of (4-x^2^{1/2}) is -x/((4-x^2)^{1/2)}