What is (\partial)/(\partial x)(xln(y)+1/9 x^3) ?

The answer to (\partial)/(\partial x)(xln(y)+1/9 x^3) is ln(y)+(x^2)/3

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(\partial)/(\partial x)(xln(y)+1/9 x^3)

\frac{\partial}{\partial x} (x ln (y) + \frac{1}{9} x^{3})

ln (y) + \frac{x ^{2}}{3}

Solution steps

\frac{\partial}{\partial x} (x ln (y) + \frac{1}{9} x^{3})

Simplify

x ln (y) + \frac{1}{9} x^{3} : x ln (y) + \frac{x ^{3}}{9}

= \frac{\partial}{\partial x} (x ln (y) + \frac{x ^{3}}{9})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x ln (y)) + \frac{\partial}{\partial x} (\frac{x ^{3}}{9})

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

\frac{\partial}{\partial x} (\frac{x ^{3}}{9}) = \frac{x ^{2}}{3}

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

x - 3

x \to 9 - lim (\frac{7}{x - 9})

\int_{0}^{π} 7 cos^{6} (x) d x

y = x sin (\frac{4}{x})

\int_{1}^{3} (1 + 2 x - 4 x^{3}) d x

What is (\partial)/(\partial x)(xln(y)+1/9 x^3) ?
The answer to (\partial)/(\partial x)(xln(y)+1/9 x^3) is ln(y)+(x^2)/3