What is (\partial)/(\partial x)(t/x) ?

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

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(\partial)/(\partial x)(t/x)

\frac{\partial}{\partial x} (\frac{t}{x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{t}{x})

Treat

t

as a constant

Take the constant out:

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

= t \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= t \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= t (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

\frac{d y}{d x} + (\frac{3}{x}) y = - 4 x - 10

\int \frac{1}{x ^{2} - 4} d x

\frac{d y}{d x} = \frac{2}{x}

\frac{d}{d x} (\frac{a}{1 + \frac{b}{x + c}})

\int 6 x^{2} d x

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