What is (\partial)/(\partial x)(e^x-xy^3) ?

The answer to (\partial)/(\partial x)(e^x-xy^3) is e^x-y^3

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(\partial)/(\partial x)(e^x-xy^3)

\frac{\partial}{\partial x} (e^{x} - x y^{3})

e^{x} - y^{3}

Solution steps

\frac{\partial}{\partial x} (e^{x} - x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (e^{x}) - \frac{\partial}{\partial x} (x y^{3})

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

\frac{\partial}{\partial x} (x y^{3}) = y^{3}

= e^{x} - y^{3}

y = - 2 x^{2}

\frac{x ^{2}}{3 + 4 x}

t \cdot e^{- 3 t} \cdot sin (5 t)

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

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

What is (\partial)/(\partial x)(e^x-xy^3) ?
The answer to (\partial)/(\partial x)(e^x-xy^3) is e^x-y^3