What is (\partial)/(\partial w)(1/(2sqrt(v-w))) ?

The answer to (\partial)/(\partial w)(1/(2sqrt(v-w))) is 1/(4(v-w)^{3/2)}

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(\partial)/(\partial w)(1/(2sqrt(v-w)))

\frac{\partial}{\partial w} (\frac{1}{2 v - w})

\frac{1}{4 ( v - w ) ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial w} (\frac{1}{2 v - w})

Treat

v

as a constant

Take the constant out:

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

= \frac{1}{2} \frac{\partial}{\partial w} (\frac{1}{v - w})

Apply exponent rule:

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

= \frac{1}{2} \frac{\partial}{\partial w} ((v - w)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} \frac{\partial}{\partial w} (v - w)

= - \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} \frac{\partial}{\partial w} (v - w)

\frac{\partial}{\partial w} (v - w) = - 1

= \frac{1}{2} (- \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} (- 1))

Simplify

\frac{1}{2} (- \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} (- 1)) : \frac{1}{4 ( v - w ) ^{\frac{3}{2}}}

= \frac{1}{4 ( v - w ) ^{\frac{3}{2}}}

\int cosh^{3} (x) d x

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\frac{\partial}{\partial x} (x^{3} sec^{2} (x y))

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(y^{11} x) \frac{d y}{d x} = 1 + x

What is (\partial)/(\partial w)(1/(2sqrt(v-w))) ?
The answer to (\partial)/(\partial w)(1/(2sqrt(v-w))) is 1/(4(v-w)^{3/2)}