What is the derivative of ((10/(4+x))^{1/2}) ?

The derivative of ((10/(4+x))^{1/2}) is -(5^{1/2})/(2^{1/2)(x+4)^{3/2}}

What is the first derivative of ((10/(4+x))^{1/2}) ?

The first derivative of ((10/(4+x))^{1/2}) is -(5^{1/2})/(2^{1/2)(x+4)^{3/2}}

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\frac{d}{d x} ((\frac{10}{4 + x})^{\frac{1}{2}})

- \frac{5 ^{\frac{1}{2}}}{2 ^{\frac{1}{2}} ( x + 4 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} ((\frac{10}{4 + x})^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( \frac{10}{4 + x} ) ^{\frac{1}{2}}} \frac{d}{d x} (\frac{10}{4 + x})

= \frac{1}{2 ( \frac{10}{4 + x} ) ^{\frac{1}{2}}} \frac{d}{d x} (\frac{10}{4 + x})

\frac{d}{d x} (\frac{10}{4 + x}) = - \frac{10}{( 4 + x ) ^{2}}

= \frac{1}{2 ( \frac{10}{4 + x} ) ^{\frac{1}{2}}} (- \frac{10}{( 4 + x ) ^{2}})

Simplify

\frac{1}{2 ( \frac{10}{4 + x} ) ^{\frac{1}{2}}} (- \frac{10}{( 4 + x ) ^{2}}) : - \frac{5 ^{\frac{1}{2}}}{2 ^{\frac{1}{2}} ( x + 4 ) ^{\frac{3}{2}}}

= - \frac{5 ^{\frac{1}{2}}}{2 ^{\frac{1}{2}} ( x + 4 ) ^{\frac{3}{2}}}

- \frac{1}{4} x^{4} + 6 x^{2}

\frac{d}{d x} (\frac{x ^{4}}{12})

f (x) = 4 x^{2} sin (x) + 2 x

cos (\frac{1 - e ^{6 x}}{1 + e ^{6 x}})

(- 9, 3), (7, - 7)

What is the derivative of ((10/(4+x))^{1/2}) ?
The derivative of ((10/(4+x))^{1/2}) is -(5^{1/2})/(2^{1/2)(x+4)^{3/2}}
What is the first derivative of ((10/(4+x))^{1/2}) ?
The first derivative of ((10/(4+x))^{1/2}) is -(5^{1/2})/(2^{1/2)(x+4)^{3/2}}