What is the derivative of f(x)= 2/(sqrt(6+8x)) ?

The derivative of f(x)= 2/(sqrt(6+8x)) is -8/((6+8x)^{3/2)}

What is the first derivative of f(x)= 2/(sqrt(6+8x)) ?

The first derivative of f(x)= 2/(sqrt(6+8x)) is -8/((6+8x)^{3/2)}

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derivative of

f (x) = \frac{2}{6 + 8 x}

- \frac{8}{( 6 + 8 x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2}{6 + 8 x})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{6 + 8 x})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((6 + 8 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 + 8 x)

= - \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 + 8 x)

\frac{d}{d x} (6 + 8 x) = 8

= 2 (- \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \cdot 8)

Simplify

2 (- \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \cdot 8) : - \frac{8}{( 6 + 8 x ) ^{\frac{3}{2}}}

= - \frac{8}{( 6 + 8 x ) ^{\frac{3}{2}}}

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x \to 0 + lim (ln (x) - \frac{1}{x})

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\frac{d}{d x} (x^{3} + 7 x - 1)

What is the derivative of f(x)= 2/(sqrt(6+8x)) ?
The derivative of f(x)= 2/(sqrt(6+8x)) is -8/((6+8x)^{3/2)}
What is the first derivative of f(x)= 2/(sqrt(6+8x)) ?
The first derivative of f(x)= 2/(sqrt(6+8x)) is -8/((6+8x)^{3/2)}