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

The derivative of 3/(4(1-x^{5/2)}) is (15)/(8(1-x)^{7/2)}

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

The first derivative of 3/(4(1-x^{5/2)}) is (15)/(8(1-x)^{7/2)}

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

\frac{15}{8 ( 1 - x ) ^{\frac{7}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= \frac{3}{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{3}{4} (- \frac{5}{2 ( 1 - x ) ^{\frac{7}{2}}} (- 1))

Simplify

\frac{3}{4} (- \frac{5}{2 ( 1 - x ) ^{\frac{7}{2}}} (- 1)) : \frac{15}{8 ( 1 - x ) ^{\frac{7}{2}}}

= \frac{15}{8 ( 1 - x ) ^{\frac{7}{2}}}

What is the derivative of 3/(4(1-x^{5/2)}) ?
The derivative of 3/(4(1-x^{5/2)}) is (15)/(8(1-x)^{7/2)}
What is the first derivative of 3/(4(1-x^{5/2)}) ?
The first derivative of 3/(4(1-x^{5/2)}) is (15)/(8(1-x)^{7/2)}