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

The answer to (\partial)/(\partial x)((e/y)^x) is (e/y)^x(1-ln(y))

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

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

(\frac{e}{y})^{x} (1 - ln (y))

Solution steps

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

Treat

y

as a constant

Apply the derivative exponent rule:

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

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

Simplify

ln (\frac{e}{y}) : - ln (y) + 1

= (\frac{e}{y})^{x} (1 - ln (y))

\int_{0}^{4} (3 t^{4} + 3 t + 2) d t

\frac{\partial}{\partial y} (2 x + 4 y)

f (x) = 2 x - 1

x \to \infty lim (e^{- x} - ln (x))

\int \frac{8 x ^{2} + x + 73}{( x + 1 ) ( x ^{2} + 9 )} d x

What is (\partial)/(\partial x)((e/y)^x) ?
The answer to (\partial)/(\partial x)((e/y)^x) is (e/y)^x(1-ln(y))