What is the derivative of 3/(8(1+x^{5/2)}) ?

The derivative of 3/(8(1+x^{5/2)}) is -(15)/(16(1+x)^{7/2)}

What is the first derivative of 3/(8(1+x^{5/2)}) ?

The first derivative of 3/(8(1+x^{5/2)}) is -(15)/(16(1+x)^{7/2)}

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\frac{d}{d x} (\frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}})

- \frac{15}{16 ( 1 + x ) ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}})

Take the constant out:

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

= \frac{3}{8} \frac{d}{d x} (\frac{1}{( 1 + x ) ^{\frac{5}{2}}})

Apply exponent rule:

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

= \frac{3}{8} \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{3}{8} (- \frac{5}{2 ( 1 + x ) ^{\frac{7}{2}}} \cdot 1)

Simplify

\frac{3}{8} (- \frac{5}{2 ( 1 + x ) ^{\frac{7}{2}}} \cdot 1) : - \frac{15}{16 ( 1 + x ) ^{\frac{7}{2}}}

= - \frac{15}{16 ( 1 + x ) ^{\frac{7}{2}}}

n = 1 \sum \infty \frac{5}{1 0 ^{n}}

y = 14 x

\int 12 tan^{11} (x) sec^{2} (x) d x

\int_{1}^{5} \frac{x ^{2} + 2}{6 x - x ^{2}} d x

\int 3 x^{2} + 4 x + 1 d x

What is the derivative of 3/(8(1+x^{5/2)}) ?
The derivative of 3/(8(1+x^{5/2)}) is -(15)/(16(1+x)^{7/2)}
What is the first derivative of 3/(8(1+x^{5/2)}) ?
The first derivative of 3/(8(1+x^{5/2)}) is -(15)/(16(1+x)^{7/2)}