What is the derivative of (1/(x^2)dx) ?

The derivative of (1/(x^2)dx) is -d/(x^2)

What is the first derivative of (1/(x^2)dx) ?

The first derivative of (1/(x^2)dx) is -d/(x^2)

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

- \frac{d}{x ^{2}}

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x ^{2}}, g = x

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= - \frac{d}{x ^{2}}

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