What is the derivative of (400/(1+1/8 sqrt(x))+200) ?

The derivative of (400/(1+1/8 sqrt(x))+200) is -(1600)/(sqrt(x)(\sqrt{x)+8)^2}

What is the first derivative of (400/(1+1/8 sqrt(x))+200) ?

The first derivative of (400/(1+1/8 sqrt(x))+200) is -(1600)/(sqrt(x)(\sqrt{x)+8)^2}

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\frac{d}{d x} (\frac{400}{1 + \frac{1}{8} x} + 200)

- \frac{1600}{x ( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{400}{1 + \frac{1}{8} x} + 200)

Simplify

\frac{400}{1 + \frac{1}{8} x} + 200 : \frac{3200}{8 + x} + 200

= \frac{d}{d x} (\frac{3200}{8 + x} + 200)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{3200}{8 + x}) + \frac{d}{d x} (200)

\frac{d}{d x} (\frac{3200}{8 + x}) = - \frac{1600}{x ( x + 8 ) ^{2}}

\frac{d}{d x} (200) = 0

= - \frac{1600}{x ( x + 8 ) ^{2}} + 0

Simplify

= - \frac{1600}{x ( x + 8 ) ^{2}}

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What is the derivative of (400/(1+1/8 sqrt(x))+200) ?
The derivative of (400/(1+1/8 sqrt(x))+200) is -(1600)/(sqrt(x)(\sqrt{x)+8)^2}
What is the first derivative of (400/(1+1/8 sqrt(x))+200) ?
The first derivative of (400/(1+1/8 sqrt(x))+200) is -(1600)/(sqrt(x)(\sqrt{x)+8)^2}