What is (\partial)/(\partial x)(3ln(x)+ln(y)) ?

The answer to (\partial)/(\partial x)(3ln(x)+ln(y)) is 3/x

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(\partial)/(\partial x)(3ln(x)+ln(y))

\frac{\partial}{\partial x} (3 ln (x) + ln (y))

\frac{3}{x}

Solution steps

\frac{\partial}{\partial x} (3 ln (x) + ln (y))

Simplify

3 ln (x) + ln (y) : ln (x^{3} y)

= \frac{\partial}{\partial x} (ln (x^{3} y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{3} y} \frac{\partial}{\partial x} (x^{3} y)

= \frac{1}{x ^{3} y} \frac{\partial}{\partial x} (x^{3} y)

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

= \frac{1}{x ^{3} y} \cdot 3 y x^{2}

Simplify

\frac{1}{x ^{3} y} \cdot 3 y x^{2} : \frac{3}{x}

= \frac{3}{x}

\frac{\partial}{\partial x} (400 e^{x y})

n = 1 \sum \infty n sin (n)

n = 1 \sum \infty \frac{5}{3 ^{2 n}}

y = 3 x^{3} - x^{2} + 6 x + 4

\int 2 x + 1 d x

What is (\partial)/(\partial x)(3ln(x)+ln(y)) ?
The answer to (\partial)/(\partial x)(3ln(x)+ln(y)) is 3/x