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

The answer to (\partial)/(\partial x)((e^x)/(y+x^5)) is (e^x(y+x^5)-5x^4e^x)/((y+x^5)^2)

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(\partial)/(\partial x)((e^x)/(y+x^5))

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

\frac{e ^{x} ( y + x ^{5} ) - 5 x ^{4} e ^{x}}{( y + x ^{5} ) ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( e ^{x} ) ( y + x ^{5} ) - \frac{\partial}{\partial x} ( y + x ^{5} ) e ^{x}}{( y + x ^{5} ) ^{2}}

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

\frac{\partial}{\partial x} (y + x^{5}) = 5 x^{4}

= \frac{e ^{x} ( y + x ^{5} ) - 5 x ^{4} e ^{x}}{( y + x ^{5} ) ^{2}}

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

\int \frac{sin ^{2} ( x )}{sin ( x ) + cos ( x )} d x

t \to 0 lim (sin (t))

\frac{d}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{5}} + 7 x^{\frac{3}{2}} - 8 x + 17)

\int arcsin^{2} (x) d x

What is (\partial)/(\partial x)((e^x)/(y+x^5)) ?
The answer to (\partial)/(\partial x)((e^x)/(y+x^5)) is (e^x(y+x^5)-5x^4e^x)/((y+x^5)^2)