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Popular >

derivative of-k/(x^2)

Solution

\frac{d}{d x} (- \frac{k}{x ^{2}})

Solution

\frac{2 k}{x ^{3}}

Solution steps

\frac{d}{d x} (- \frac{k}{x ^{2}})

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - k (- 2 x^{- 2 - 1})

Simplify

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

= \frac{2 k}{x ^{3}}

Popular Examples

integral of (2x+3)/(x+1)

\int \frac{2 x + 3}{x + 1} d x

integral of (x^2)/(\sqrt[4]{x^3+4)}

derivative of x^3-8x^2+19x-12 derivative of

x^{3} - 8 x^{2} + 19 x - 12

integral from 5 to 10 of (3x+3)

\int_{5}^{10} (3 x + 3) d x

(\partial)/(\partial y)(x^3-y^2+2xy)

\frac{\partial}{\partial y} (x^{3} - y^{2} + 2 x y)

Frequently Asked Questions (FAQ)

What is the derivative of-k/(x^2) ?
The derivative of-k/(x^2) is (2k)/(x^3)
What is the first derivative of-k/(x^2) ?
The first derivative of-k/(x^2) is (2k)/(x^3)