What is (\partial)/(\partial x)(z-e^{xy}) ?

The answer to (\partial)/(\partial x)(z-e^{xy}) is -e^{xy}y

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(\partial)/(\partial x)(z-e^{xy})

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

- e^{x y} y

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (z) = 0

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

= 0 - e^{x y} y

Simplify

= - e^{x y} y

ln (\frac{( e ^{x} + 1 )}{e ^{x} - 1})

y^{^{''}} - 6 y^{^{'}} - 7 y = 0, y (2) = - \frac{1}{3}, y^{^{'}} (0) = 0

5 + \frac{7}{x}

\int \frac{sin ( x )}{x} d x

\int_{6}^{8} \frac{90}{( x - 6 ) ^{3}} d x

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