What is (\partial)/(\partial x)(x^2y)+ln(xy^2) ?

The solution to (\partial)/(\partial x)(x^2y)+ln(xy^2) is (\partial)/(\partial x)(x^2y)+ln(x)+2ln(y)

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simplify (\partial)/(\partial x)(x^2y)+ln(xy^2)

simplify

\frac{\partial}{\partial x} (x^{2} y) + ln (x y^{2})

\frac{\partial}{\partial x} (x^{2} y) + ln (x) + 2 ln (y)

Solution steps

\frac{\partial}{\partial x} (x^{2} y) + ln (x y^{2})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x y^{2}) = ln (x) + ln (y^{2})

= \frac{\partial}{\partial x} (x^{2} y) + ln (x) + ln (y^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (y^{2}) = 2 ln (y)

= \frac{\partial}{\partial x} (x^{2} y) + ln (x) + 2 ln (y)

ln (\frac{( 1 + e ^{x} )}{( 1 - e ^{x} )})

lo g_{b} (\frac{a ^{2} b ^{3}}{c ^{4} m})

4 ln (x) + 4 ln (y)

lo g_{8} (2 x^{3})

lo g_{10} (9 x)

What is (\partial)/(\partial x)(x^2y)+ln(xy^2) ?
The solution to (\partial)/(\partial x)(x^2y)+ln(xy^2) is (\partial)/(\partial x)(x^2y)+ln(x)+2ln(y)