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Popular >

derivative of y= 4/x+sqrt(x+0.5)-5x

Solution

derivative of

y = \frac{4}{x} + x + 0.5 - 5 x

Solution

- \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

Solution steps

\frac{d}{d x} (\frac{4}{x} + x + 0.5 - 5 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (x + 0.5) - \frac{d}{d x} (5 x)

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{d}{d x} (x + 0.5) = \frac{0.5}{x + 0.5}

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

= - \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

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Frequently Asked Questions (FAQ)

What is the derivative of y= 4/x+sqrt(x+0.5)-5x ?
The derivative of y= 4/x+sqrt(x+0.5)-5x is -4/(x^2)+(0.5)/(sqrt(x+0.5))-5
What is the first derivative of y= 4/x+sqrt(x+0.5)-5x ?
The first derivative of y= 4/x+sqrt(x+0.5)-5x is -4/(x^2)+(0.5)/(sqrt(x+0.5))-5