What is (\partial)/(\partial y)(4e^xln(y)) ?

The answer to (\partial)/(\partial y)(4e^xln(y)) is (4e^x)/y

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(\partial)/(\partial y)(4e^xln(y))

\frac{\partial}{\partial y} (4 e^{x} ln (y))

\frac{4 e ^{x}}{y}

Solution steps

\frac{\partial}{\partial y} (4 e^{x} ln (y))

Treat

x

as a constant

Take the constant out:

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

= 4 e^{x} \frac{\partial}{\partial y} (ln (y))

Apply the common derivative:

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

= 4 e^{x} \frac{1}{y}

Simplify

4 e^{x} \frac{1}{y} : \frac{4 e ^{x}}{y}

= \frac{4 e ^{x}}{y}

\frac{d}{d x} (x - \frac{1}{x})

\frac{d y}{d x} = e^{4 x - y}

\frac{d}{d x} (- x^{4})

h \to 0 lim (\frac{( - 4 + h ) + 4}{h})

\int \frac{8 x ^{2} + 5 x + 8}{( x ^{2} + 1 ) ^{2}} d x

What is (\partial)/(\partial y)(4e^xln(y)) ?
The answer to (\partial)/(\partial y)(4e^xln(y)) is (4e^x)/y