What is (\partial)/(\partial x)(0.5ln(x)+0.5ln(y)) ?

The answer to (\partial)/(\partial x)(0.5ln(x)+0.5ln(y)) is (0.5)/(x^{1/2)sqrt(x)}

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(\partial)/(\partial x)(0.5ln(x)+0.5ln(y))

\frac{\partial}{\partial x} (0.5 ln (x) + 0.5 ln (y))

\frac{0.5}{x ^{\frac{1}{2}} x}

Solution steps

\frac{\partial}{\partial x} (0.5 ln (x) + 0.5 ln (y))

Simplify

0.5 ln (x) + 0.5 ln (y) : ln (x^{0.5} y^{0.5})

= \frac{\partial}{\partial x} (ln (x^{0.5} y^{0.5}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{0.5} y ^{0.5}} \frac{\partial}{\partial x} (x^{0.5} y^{0.5})

= \frac{1}{x ^{0.5} y ^{0.5}} \frac{\partial}{\partial x} (x^{0.5} y^{0.5})

\frac{\partial}{\partial x} (x^{0.5} y^{0.5}) = \frac{0.5 y ^{\frac{1}{2}}}{x}

= \frac{1}{x ^{0.5} y ^{0.5}} \cdot \frac{0.5 y ^{\frac{1}{2}}}{x}

Simplify

\frac{1}{x ^{\frac{1}{2}} y ^{\frac{1}{2}}} \cdot \frac{0.5 y ^{\frac{1}{2}}}{x} : \frac{0.5}{x ^{\frac{1}{2}} x}

= \frac{0.5}{x ^{\frac{1}{2}} x}

\int e^{8 t} d t

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

t^{2} - 2 t

- \frac{7}{4 x}

\int \frac{x ^{4}}{8 - x ^{5}} d x

What is (\partial)/(\partial x)(0.5ln(x)+0.5ln(y)) ?
The answer to (\partial)/(\partial x)(0.5ln(x)+0.5ln(y)) is (0.5)/(x^{1/2)sqrt(x)}