What is the first d/(dv)(u/v) ?

The first d/(dv)(u/v) is -u/(v^2)

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d/(dv)(u/v)

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

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

Solution steps

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

Treat

u

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

= u \frac{d}{d 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}}

\int_{0}^{1} - 2 (x^{2} + 1) e^{- x} d x

f (x) = arcsec (2 x)

5 t - 3

\frac{\partial}{\partial x} ((x + y)^{8})

r^{2} - 6 x^{2}