What is (\partial)/(\partial y)(x^yln(x)) ?

The answer to (\partial)/(\partial y)(x^yln(x)) is x^yln^2(x)

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(\partial)/(\partial y)(x^yln(x))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

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

Simplify

ln (x) x^{y} ln (x) : x^{y} ln^{2} (x)

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

\int_{0}^{34} x^{2} - 17 d x

\frac{\partial}{\partial y} (x y + 3 x - 2 y)

\int_{0}^{1} x^{2} + 2 d x

\int \frac{tan ( \frac{2}{x} )}{x ^{2}} d x

n = 1 \sum \infty \frac{2 n + 1}{7 ^{n}}

What is (\partial)/(\partial y)(x^yln(x)) ?
The answer to (\partial)/(\partial y)(x^yln(x)) is x^yln^2(x)