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

The derivative of-3/(2(1+x^{3/2)}) is 9/(4(1+x)^{5/2)}

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

The first derivative of-3/(2(1+x^{3/2)}) is 9/(4(1+x)^{5/2)}

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

\frac{9}{4 ( 1 + x ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

- \frac{3}{2} (- \frac{3}{2 ( 1 + x ) ^{\frac{5}{2}}} \cdot 1) : \frac{9}{4 ( 1 + x ) ^{\frac{5}{2}}}

= \frac{9}{4 ( 1 + x ) ^{\frac{5}{2}}}

\frac{d}{d x} (1 ln (x) - \frac{x ^{2}}{8})

g (u) = 6 u + 5 u

\int \frac{4}{5} - \frac{1}{3 5 x} d x

\int 12 θ sec^{2} (θ) d θ

x e^{- x}

What is the derivative of-3/(2(1+x^{3/2)}) ?
The derivative of-3/(2(1+x^{3/2)}) is 9/(4(1+x)^{5/2)}
What is the first derivative of-3/(2(1+x^{3/2)}) ?
The first derivative of-3/(2(1+x^{3/2)}) is 9/(4(1+x)^{5/2)}