What is the derivative of (2.4)/(sqrt(5+1x)) ?

The derivative of (2.4)/(sqrt(5+1x)) is -(1.2)/((5+x)^{3/2)}

What is the first derivative of (2.4)/(sqrt(5+1x)) ?

The first derivative of (2.4)/(sqrt(5+1x)) is -(1.2)/((5+x)^{3/2)}

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derivative of

\frac{2.4}{5 + 1 x}

- \frac{1.2}{( 5 + x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2.4}{5 + 1 \cdot x})

Take the constant out:

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

= 2.4 \frac{d}{d x} (\frac{1}{5 + 1 \cdot x})

Apply exponent rule:

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

= 2.4 \frac{d}{d x} ((5 + 1 \cdot x)^{- \frac{1}{2}})

Apply the chain rule:

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

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

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

= 2.4 (- \frac{1}{2 ( 5 + 1 \cdot x ) ^{\frac{3}{2}}} \cdot 1)

Simplify

2.4 (- \frac{1}{2 ( 5 + 1 \cdot x ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1.2}{( 5 + x ) ^{\frac{3}{2}}}

= - \frac{1.2}{( 5 + x ) ^{\frac{3}{2}}}

What is the derivative of (2.4)/(sqrt(5+1x)) ?
The derivative of (2.4)/(sqrt(5+1x)) is -(1.2)/((5+x)^{3/2)}
What is the first derivative of (2.4)/(sqrt(5+1x)) ?
The first derivative of (2.4)/(sqrt(5+1x)) is -(1.2)/((5+x)^{3/2)}