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

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

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

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

2 y x + \frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (ln (x)) = \frac{1}{x}

= 2 y x + \frac{1}{x}

7 x^{2} - 3 x, x^{2} - 7 x + 2

x \to + 0 + lim (\frac{e ^{x}}{e ^{x} - 1})

\int \frac{28 e ^{4 t}}{6 + e ^{4 t}} d t

1 + cos (θ)

\frac{\partial}{\partial x} (3 x^{7} y^{8} + 8 x^{5} y^{6})

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