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Popular Calculus >

derivative of f(x)= 7/x-sqrt(x)

Solution

derivative of

f (x) = \frac{7}{x} - x

Solution

- \frac{x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

Solution steps

\frac{d}{d x} (\frac{7}{x} - x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{7}{x}) - \frac{d}{d x} (x)

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{x ^{2}}

\frac{d}{d x} (x) = \frac{1}{2 x}

= - \frac{7}{x ^{2}} - \frac{1}{2 x}

Simplify

- \frac{7}{x ^{2}} - \frac{1}{2 x} : - \frac{x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

= - \frac{x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)= 7/x-sqrt(x) ?
The derivative of f(x)= 7/x-sqrt(x) is -(x^{3/2}+14)/(2x^{3/2)sqrt(x)}
What is the first derivative of f(x)= 7/x-sqrt(x) ?
The first derivative of f(x)= 7/x-sqrt(x) is -(x^{3/2}+14)/(2x^{3/2)sqrt(x)}