What is (\partial)/(\partial x)(ex^3-y^5) ?

The answer to (\partial)/(\partial x)(ex^3-y^5) is 3ex^2

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(\partial)/(\partial x)(ex^3-y^5)

\frac{\partial}{\partial x} (e x^{3} - y^{5})

3 e x^{2}

Solution steps

\frac{\partial}{\partial x} (e x^{3} - y^{5})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e x^{3}) - \frac{\partial}{\partial x} (y^{5})

\frac{\partial}{\partial x} (e x^{3}) = 3 e x^{2}

\frac{\partial}{\partial x} (y^{5}) = 0

= 3 e x^{2} - 0

Simplify

= 3 e x^{2}

f (x) = x^{e^{x}}

\frac{d}{d x} (4^{2 x})

f (x) = \frac{8 x ^{2} + 8 x + 2}{x}

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

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

What is (\partial)/(\partial x)(ex^3-y^5) ?
The answer to (\partial)/(\partial x)(ex^3-y^5) is 3ex^2