What is the derivative of f(x)= 1/(sqrt(x+8)) ?

The derivative of f(x)= 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}

What is the first derivative of f(x)= 1/(sqrt(x+8)) ?

The first derivative of f(x)= 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}

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derivative of

f (x) = \frac{1}{x + 8}

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x + 8})

Apply exponent rule:

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

= \frac{d}{d x} ((x + 8)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}}

y^{^{'}} - y = x e^{2 x} + 1

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

x y^{^{'}} = 4 x^{2} - 2 y, y (1) = 3

y^{2} - 27 x = 0, x + y = 0

f (x) = x^{3} + 4 x - 2, at x = 1

What is the derivative of f(x)= 1/(sqrt(x+8)) ?
The derivative of f(x)= 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}
What is the first derivative of f(x)= 1/(sqrt(x+8)) ?
The first derivative of f(x)= 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}