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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

Simplify

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

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

\int arccos (4 x) d x

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

\frac{\partial}{\partial x} (x^{2} + y^{2} - z)

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

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

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