What is the derivative of-(20000/(sqrt(1+0.2x))) ?

The derivative of-(20000/(sqrt(1+0.2x))) is (2000)/((1+0.2x)^{3/2)}

What is the first derivative of-(20000/(sqrt(1+0.2x))) ?

The first derivative of-(20000/(sqrt(1+0.2x))) is (2000)/((1+0.2x)^{3/2)}

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\frac{d}{d x} (- \frac{20000}{1 + 0.2 x})

\frac{2000}{( 1 + 0.2 x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (- \frac{20000}{1 + 0.2 x})

Take the constant out:

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

= - 20000 \frac{d}{d x} (\frac{1}{1 + 0.2 x})

Apply exponent rule:

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

= - 20000 \frac{d}{d x} ((1 + 0.2 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 1 + 0.2 x ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + 0.2 x)

= - \frac{1}{2 ( 1 + 0.2 x ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + 0.2 x)

\frac{d}{d x} (1 + 0.2 x) = 0.2

= - 20000 (- \frac{1}{2 ( 1 + 0.2 x ) ^{\frac{3}{2}}} \cdot 0.2)

Simplify

- 20000 (- \frac{1}{2 ( 1 + 0.2 x ) ^{\frac{3}{2}}} \cdot 0.2) : \frac{2000}{( 1 + 0.2 x ) ^{\frac{3}{2}}}

= \frac{2000}{( 1 + 0.2 x ) ^{\frac{3}{2}}}

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What is the derivative of-(20000/(sqrt(1+0.2x))) ?
The derivative of-(20000/(sqrt(1+0.2x))) is (2000)/((1+0.2x)^{3/2)}
What is the first derivative of-(20000/(sqrt(1+0.2x))) ?
The first derivative of-(20000/(sqrt(1+0.2x))) is (2000)/((1+0.2x)^{3/2)}