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Popular >

derivative of 1/(5x^4-5/(2x))

Solution

\frac{d}{d x} (\frac{1}{5 x ^{4}} - \frac{5}{2 x})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{5 x ^{4}} - \frac{5}{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{5 x ^{4}}) - \frac{d}{d x} (\frac{5}{2 x})

\frac{d}{d x} (\frac{1}{5 x ^{4}}) = - \frac{4}{5 x ^{5}}

\frac{d}{d x} (\frac{5}{2 x}) = - \frac{5}{2 x ^{2}}

= - \frac{4}{5 x ^{5}} - (- \frac{5}{2 x ^{2}})

Simplify

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

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x \to - \infty lim (e^{5 x})

Frequently Asked Questions (FAQ)

What is the derivative of 1/(5x^4-5/(2x)) ?
The derivative of 1/(5x^4-5/(2x)) is -4/(5x^5)+5/(2x^2)
What is the first derivative of 1/(5x^4-5/(2x)) ?
The first derivative of 1/(5x^4-5/(2x)) is -4/(5x^5)+5/(2x^2)