What is (\partial)/(\partial y)((4ln(y+2))/(xe^x)) ?

The answer to (\partial)/(\partial y)((4ln(y+2))/(xe^x)) is 4/(e^xx(y+2))

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(\partial)/(\partial y)((4ln(y+2))/(xe^x))

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

\frac{4}{e ^{x} x ( y + 2 )}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= \frac{4}{x e ^{x}} \frac{\partial}{\partial y} (ln (y + 2))

Apply the chain rule:

\frac{1}{y + 2} \frac{\partial}{\partial y} (y + 2)

= \frac{1}{y + 2} \frac{\partial}{\partial y} (y + 2)

\frac{\partial}{\partial y} (y + 2) = 1

= \frac{4}{x e ^{x}} \cdot \frac{1}{y + 2} \cdot 1

Simplify

\frac{4}{x e ^{x}} \cdot \frac{1}{y + 2} \cdot 1 : \frac{4}{e ^{x} x ( y + 2 )}

= \frac{4}{e ^{x} x ( y + 2 )}

\int 7 x d x

\frac{4}{( x ^{2} - 1 ) ^{4}}

\frac{6}{5 x + 2}, at a = - 1

y^{^{'}} + 6 y = 60, y (1) = 90

f (x) = tan (x^{2} + 3 x - 4)

What is (\partial)/(\partial y)((4ln(y+2))/(xe^x)) ?
The answer to (\partial)/(\partial y)((4ln(y+2))/(xe^x)) is 4/(e^xx(y+2))