What is (\partial)/(\partial y)(4y(1/x-ln(x))) ?

The answer to (\partial)/(\partial y)(4y(1/x-ln(x))) is 4(1/x-ln(x))

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(\partial)/(\partial y)(4y(1/x-ln(x)))

\frac{\partial}{\partial y} (4 y (\frac{1}{x} - ln (x)))

4 (\frac{1}{x} - ln (x))

Solution steps

\frac{\partial}{\partial y} (4 y (\frac{1}{x} - ln (x)))

Treat

x

as a constant

Take the constant out:

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

= 4 (\frac{1}{x} - ln (x)) \frac{\partial}{\partial y} (y)

Apply the common derivative:

\frac{\partial}{\partial y} (y) = 1

= 4 (\frac{1}{x} - ln (x)) \cdot 1

Simplify

= 4 (\frac{1}{x} - ln (x))

What is (\partial)/(\partial y)(4y(1/x-ln(x))) ?
The answer to (\partial)/(\partial y)(4y(1/x-ln(x))) is 4(1/x-ln(x))