What is (\partial)/(\partial x)(x^5+4z^2e^{y-x}) ?

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

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(\partial)/(\partial x)(x^5+4z^2e^{y-x})

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

5 x^{4} - 4 z^{2} e^{y - x}

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 z^{2} e^{y - x}) = - 4 z^{2} e^{y - x}

= 5 x^{4} - 4 z^{2} e^{y - x}

\int x^{3} e^{- \frac{x}{3}} d x

x^{4}, x

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

\frac{\frac{E}{L}}{( s ^{2} + \frac{1}{C L} )}

y = x^{π}

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