What is the derivative of (sqrt(x)+1/(sqrt(x^3))^2) ?

The derivative of (sqrt(x)+1/(sqrt(x^3))^2) is 1-(2x^2+3)/(x^4)

What is the first derivative of (sqrt(x)+1/(sqrt(x^3))^2) ?

The first derivative of (sqrt(x)+1/(sqrt(x^3))^2) is 1-(2x^2+3)/(x^4)

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

1 - \frac{2 x ^{2} + 3}{x ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 (x + \frac{1}{x ^{3}}) (\frac{1}{2 x} - \frac{3 x ^{2}}{2 ( x ^{3} ) ^{\frac{3}{2}}}) : 1 - \frac{2 x ^{2} + 3}{x ^{4}}

= 1 - \frac{2 x ^{2} + 3}{x ^{4}}

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

y = \frac{4 x ^{2} + 8 x + 4}{x}

x \to 5 lim (5 - x)

k = 0 \sum \infty \frac{1}{2} \cdot (- 1)^{k}

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

What is the derivative of (sqrt(x)+1/(sqrt(x^3))^2) ?
The derivative of (sqrt(x)+1/(sqrt(x^3))^2) is 1-(2x^2+3)/(x^4)
What is the first derivative of (sqrt(x)+1/(sqrt(x^3))^2) ?
The first derivative of (sqrt(x)+1/(sqrt(x^3))^2) is 1-(2x^2+3)/(x^4)