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Popular >

(\partial)/(\partial v)(u/v)

Solution

\frac{\partial}{\partial v} (\frac{u}{v})

Solution

- \frac{u}{v ^{2}}

Solution steps

\frac{\partial}{\partial v} (\frac{u}{v})

Treat

u

as a constant

Take the constant out:

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

= u \frac{\partial}{\partial v} (\frac{1}{v})

Apply exponent rule:

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

= u \frac{\partial}{\partial v} (v^{- 1})

Apply the Power Rule:

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

= u (- 1 \cdot v^{- 1 - 1})

Simplify

u (- 1 \cdot v^{- 1 - 1}) : - \frac{u}{v ^{2}}

= - \frac{u}{v ^{2}}

Popular Examples

y*ln(x)-x^2y=xy^'

y \cdot ln (x) - x^{2} y = x y^{^{'}}

(\partial)/(\partial x)(ln(x+y^4)-z)

\frac{\partial}{\partial x} (ln (x + y^{4}) - z)

integral of (3x^2-2x+3)

\int (3 x^{2} - 2 x + 3) d x

integral of 1/4-(100)/(x^2)

\int \frac{1}{4} - \frac{100}{x ^{2}} d x

derivative of sin(x^2cos(x^2))

\frac{d}{d x} (sin (x^{2}) cos (x^{2}))

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial v)(u/v) ?
The answer to (\partial)/(\partial v)(u/v) is -u/(v^2)