What is the derivative of-1/(2(1+x^{3/2)}) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + x) = 1

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

Simplify

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

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

f (x) = - \frac{6}{( 1 + 3 x ) ^{2}}

\frac{d}{d x} (ln (\frac{( 2 )}{3 - x ^{2}}))

\frac{3}{t ^{3}}

n = 0 \sum \infty \frac{x ^{2 n}}{n !}

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