What is the derivative of 7/(sqrt(x+2)) ?

The derivative of 7/(sqrt(x+2)) is -7/(2(x+2)^{3/2)}

What is the first derivative of 7/(sqrt(x+2)) ?

The first derivative of 7/(sqrt(x+2)) is -7/(2(x+2)^{3/2)}

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\frac{d}{d x} (\frac{7}{x + 2})

- \frac{7}{2 ( x + 2 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{7}{x + 2})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{1}{x + 2})

Apply exponent rule:

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

= 7 \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

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

Simplify

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

= - \frac{7}{2 ( x + 2 ) ^{\frac{3}{2}}}

\frac{2 x + 1}{x + 2}, at a = 1

\int \frac{x ^{2}}{7 - x ^{3}} d x

\int \frac{8}{1 + 9 x ^{2}} d x

x \to 0 lim (\frac{tan ( x ) + x}{x})

n = 0 \sum \infty 3 (- \frac{1}{4})^{n - 1}

What is the derivative of 7/(sqrt(x+2)) ?
The derivative of 7/(sqrt(x+2)) is -7/(2(x+2)^{3/2)}
What is the first derivative of 7/(sqrt(x+2)) ?
The first derivative of 7/(sqrt(x+2)) is -7/(2(x+2)^{3/2)}