What is (\partial)/(\partial y)(5e^xln(y)) ?

The answer to (\partial)/(\partial y)(5e^xln(y)) is (5e^x)/y

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(\partial)/(\partial y)(5e^xln(y))

\frac{\partial}{\partial y} (5 e^{x} ln (y))

\frac{5 e ^{x}}{y}

Solution steps

\frac{\partial}{\partial y} (5 e^{x} ln (y))

Treat

x

as a constant

Take the constant out:

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

= 5 e^{x} \frac{\partial}{\partial y} (ln (y))

Apply the common derivative:

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

= 5 e^{x} \frac{1}{y}

Simplify

5 e^{x} \frac{1}{y} : \frac{5 e ^{x}}{y}

= \frac{5 e ^{x}}{y}

\frac{d}{d x} (e^{x} (sin (x) + cos (x)))

x^{3} - 2 x^{2} + 3 x + 5 (2)

\int_{e^{2}}^{e^{5}} (\frac{1}{x}) d x

(2, 5), (0, - 9)

\frac{u}{u ^{2} + 5}

What is (\partial)/(\partial y)(5e^xln(y)) ?
The answer to (\partial)/(\partial y)(5e^xln(y)) is (5e^x)/y