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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

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

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

f (x) = sinh^{2} (x)

f^{^{'}} (x) = x^{2} - x - 2

y = ∣ 7 x ∣, y = x^{2} - 8

6 e^{x}

\frac{d y}{d x} = 5 y + a

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