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Popular >

(\partial)/(\partial x)(3/(x^3))

Solution

\frac{\partial}{\partial x} (\frac{3}{x ^{3}})

Solution

- \frac{9}{x ^{4}}

Solution steps

\frac{\partial}{\partial x} (\frac{3}{x ^{3}})

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= 3 \frac{\partial}{\partial x} (x^{- 3})

Apply the Power Rule:

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

= 3 (- 3 x^{- 3 - 1})

Simplify

3 (- 3 x^{- 3 - 1}) : - \frac{9}{x ^{4}}

= - \frac{9}{x ^{4}}

Popular Examples

derivative of (e^x/(8x^2+7))

\frac{d}{d x} (\frac{e ^{x}}{8 x ^{2} + 7})

derivative of f(x)=x(1/x)derivative of

f (x) = x (\frac{1}{x})

\int 15 d x

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\frac{d}{d x} (4 x^{3} + 6 x^{2} - 5)

(\partial)/(\partial x)(x^4-4x^3y+6x^2y^2)

\frac{\partial}{\partial x} (x^{4} - 4 x^{3} y + 6 x^{2} y^{2})

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(3/(x^3)) ?
The answer to (\partial)/(\partial x)(3/(x^3)) is -9/(x^4)