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

The derivative of-(45/(8(1+x)^{7/2)}) is (315)/(16(1+x)^{9/2)}

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

The first derivative of-(45/(8(1+x)^{7/2)}) is (315)/(16(1+x)^{9/2)}

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

\frac{315}{16 ( 1 + x ) ^{\frac{9}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{7}{2 ( 1 + x ) ^{\frac{9}{2}}} \frac{d}{d x} (1 + x)

= - \frac{7}{2 ( 1 + x ) ^{\frac{9}{2}}} \frac{d}{d x} (1 + x)

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

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

Simplify

- \frac{45}{8} (- \frac{7}{2 ( 1 + x ) ^{\frac{9}{2}}} \cdot 1) : \frac{315}{16 ( 1 + x ) ^{\frac{9}{2}}}

= \frac{315}{16 ( 1 + x ) ^{\frac{9}{2}}}

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x \to 0 lim (x^{\frac{1}{1 - x}})

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What is the derivative of-(45/(8(1+x)^{7/2)}) ?
The derivative of-(45/(8(1+x)^{7/2)}) is (315)/(16(1+x)^{9/2)}
What is the first derivative of-(45/(8(1+x)^{7/2)}) ?
The first derivative of-(45/(8(1+x)^{7/2)}) is (315)/(16(1+x)^{9/2)}