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Popular >

derivative of x/5-5/x

Solution

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

Solution

\frac{1}{5} + \frac{5}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

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

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

Simplify

= \frac{1}{5} + \frac{5}{x ^{2}}

Graph

Popular Examples

(\partial)/(\partial p)(ln((p+q)/(q^2)))

\frac{\partial}{\partial p} (ln (\frac{p + q}{q ^{2}}))

derivative of (2x+1)^3+1/((2x+1)^3)derivative of

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

sum from n=0 to infinity of 5/(e^{2n)}

n = 0 \sum \infty \frac{5}{e ^{2 n}}

derivative of e^{x-1}-1

\frac{d}{d x} (e^{x - 1} - 1)

\frac{d y}{d x} = x^{8} y

Frequently Asked Questions (FAQ)

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