What is the derivative of 3/(sqrt(x+2)) ?

The derivative of 3/(sqrt(x+2)) is -3/(2(x+2)^{3/2)}

What is the first derivative of 3/(sqrt(x+2)) ?

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

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\frac{d}{d x} (\frac{3}{x + 2})

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

Solution steps

\frac{d}{d x} (\frac{3}{x + 2})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{4}{y ^{2} + 5 y - 14} d y

\int_{0}^{21} - x (x - 21) (x + 1) d x

\frac{d}{d x} ((x)^{x})

y^{^{'}} + \frac{y}{10} = 500

\frac{d N}{d t} = N (1 - 0.0002 N)

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