What is (\partial)/(\partial x)(-x^4) ?

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

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(\partial)/(\partial x)(-x^4)

\frac{\partial}{\partial x} (- x^{4})

- 4 x^{3}

Solution steps

\frac{\partial}{\partial x} (- x^{4})

Take the constant out:

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

= - \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

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

= - 4 x^{4 - 1}

Simplify

= - 4 x^{3}

x^{2} y^{^{''}} + 3 x y^{^{'}} + y = 0, y (1) = 3.6, y^{^{'}} (1) = 0.4

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