What is the derivative of-(0.4/(sqrt(5+5x))) ?

The derivative of-(0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}

What is the first derivative of-(0.4/(sqrt(5+5x))) ?

The first derivative of-(0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}

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\frac{d}{d x} (- \frac{0.4}{5 + 5 x})

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

Solution steps

\frac{d}{d x} (- \frac{0.4}{5 + 5 x})

Take the constant out:

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

= - 0.4 \frac{d}{d x} (\frac{1}{5 + 5 x})

Apply exponent rule:

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

= - 0.4 \frac{d}{d x} ((5 + 5 x)^{- \frac{1}{2}})

Apply the chain rule:

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

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

\frac{d}{d x} (5 + 5 x) = 5

= - 0.4 (- \frac{1}{2 ( 5 + 5 x ) ^{\frac{3}{2}}} \cdot 5)

Simplify

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

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

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What is the derivative of-(0.4/(sqrt(5+5x))) ?
The derivative of-(0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}
What is the first derivative of-(0.4/(sqrt(5+5x))) ?
The first derivative of-(0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}