What is the derivative of (x-1/x ^{5/2}) ?

The derivative of (x-1/x ^{5/2}) is (5(x^2+1)(x^2-1)^{3/2})/(2x^{7/2)}

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

The first derivative of (x-1/x ^{5/2}) is (5(x^2+1)(x^2-1)^{3/2})/(2x^{7/2)}

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

\frac{5 ( x ^{2} + 1 ) ( x ^{2} - 1 ) ^{\frac{3}{2}}}{2 x ^{\frac{7}{2}}}

Solution steps

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

Apply the chain rule:

\frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} \frac{d}{d x} (x - \frac{1}{x})

= \frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} \frac{d}{d x} (x - \frac{1}{x})

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

= \frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} (1 + \frac{1}{x ^{2}})

Simplify

\frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} (1 + \frac{1}{x ^{2}}) : \frac{5 ( x ^{2} + 1 ) ( x ^{2} - 1 ) ^{\frac{3}{2}}}{2 x ^{\frac{7}{2}}}

= \frac{5 ( x ^{2} + 1 ) ( x ^{2} - 1 ) ^{\frac{3}{2}}}{2 x ^{\frac{7}{2}}}

d er i v a t i v e y = (\frac{2 x - 3}{( x ^{2} + 4 ) ^{2}})

s l o p e in t erce pt (1, 4), (4, 1)

d er i v a t i v e y = (2 x + e^{- x^{2}})^{3}

\frac{d P}{d t} = P (a - b P)

a re a y = 2 x, y = 2 x^{2} - 4

What is the derivative of (x-1/x ^{5/2}) ?
The derivative of (x-1/x ^{5/2}) is (5(x^2+1)(x^2-1)^{3/2})/(2x^{7/2)}
What is the first derivative of (x-1/x ^{5/2}) ?
The first derivative of (x-1/x ^{5/2}) is (5(x^2+1)(x^2-1)^{3/2})/(2x^{7/2)}