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

The derivative of 9/(4(1+x^{5/2)}) is -(45)/(8(1+x)^{7/2)}

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

The first derivative of 9/(4(1+x^{5/2)}) is -(45)/(8(1+x)^{7/2)}

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

- \frac{45}{8 ( 1 + x ) ^{\frac{7}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{5}{2 ( 1 + x ) ^{\frac{7}{2}}} \frac{d}{d x} (1 + x)

= - \frac{5}{2 ( 1 + x ) ^{\frac{7}{2}}} \frac{d}{d x} (1 + x)

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

= \frac{9}{4} (- \frac{5}{2 ( 1 + x ) ^{\frac{7}{2}}} \cdot 1)

Simplify

\frac{9}{4} (- \frac{5}{2 ( 1 + x ) ^{\frac{7}{2}}} \cdot 1) : - \frac{45}{8 ( 1 + x ) ^{\frac{7}{2}}}

= - \frac{45}{8 ( 1 + x ) ^{\frac{7}{2}}}

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What is the derivative of 9/(4(1+x^{5/2)}) ?
The derivative of 9/(4(1+x^{5/2)}) is -(45)/(8(1+x)^{7/2)}
What is the first derivative of 9/(4(1+x^{5/2)}) ?
The first derivative of 9/(4(1+x^{5/2)}) is -(45)/(8(1+x)^{7/2)}