What is (\partial)/(\partial b)(a/b) ?

The answer to (\partial)/(\partial b)(a/b) is -a/(b^2)

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(\partial)/(\partial b)(a/b)

\frac{\partial}{\partial b} (\frac{a}{b})

- \frac{a}{b ^{2}}

Solution steps

\frac{\partial}{\partial b} (\frac{a}{b})

Take the constant out:

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

= a \frac{\partial}{\partial b} (\frac{1}{b})

Apply exponent rule:

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

= a \frac{\partial}{\partial b} (b^{- 1})

Apply the Power Rule:

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

= a (- 1 \cdot b^{- 1 - 1})

Simplify

a (- 1 \cdot b^{- 1 - 1}) : - \frac{a}{b ^{2}}

= - \frac{a}{b ^{2}}

\int \frac{7 - 98 x}{16 - 49 x ^{2}} d x

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\int t^{24} e^{- t^{25}} d t

x \to 0 lim ((x)^{3 x})

What is (\partial)/(\partial b)(a/b) ?
The answer to (\partial)/(\partial b)(a/b) is -a/(b^2)