What is (\partial)/(\partial x)(y/(h^2x)) ?

The answer to (\partial)/(\partial x)(y/(h^2x)) is -y/(h^2x^2)

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(\partial)/(\partial x)(y/(h^2x))

\frac{\partial}{\partial x} (\frac{y}{h ^{2} x})

- \frac{y}{h ^{2} x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{y}{h ^{2} x})

Treat

y, h

as constants

Take the constant out:

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

= \frac{y}{h ^{2}} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= \frac{y}{h ^{2}} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= \frac{y}{h ^{2}} (- 1 \cdot x^{- 1 - 1})

Simplify

\frac{y}{h ^{2}} (- 1 \cdot x^{- 1 - 1}) : - \frac{y}{h ^{2} x ^{2}}

= - \frac{y}{h ^{2} x ^{2}}

y^{^{'}} = 2 y (1 - 3 y)

t y^{^{'}} - y = 0

ln (x), y = 2, 1, e^{2}

\frac{d}{d x} (3 4 - x)

\frac{d r}{d t} = - 4 r t

What is (\partial)/(\partial x)(y/(h^2x)) ?
The answer to (\partial)/(\partial x)(y/(h^2x)) is -y/(h^2x^2)