What is (\partial)/(\partial x)(e^{xyz-6}) ?

The answer to (\partial)/(\partial x)(e^{xyz-6}) is e^{xyz-6}yz

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(\partial)/(\partial x)(e^{xyz-6})

\frac{\partial}{\partial x} (e^{x yz - 6})

e^{x yz - 6} yz

Solution steps

\frac{\partial}{\partial x} (e^{x yz - 6})

Treat

y, z

as constants

Apply the chain rule:

e^{x yz - 6} \frac{\partial}{\partial x} (x yz - 6)

= e^{x yz - 6} \frac{\partial}{\partial x} (x yz - 6)

\frac{\partial}{\partial x} (x yz - 6) = yz

= e^{x yz - 6} yz

\frac{d}{d x} (\frac{x ^{9}}{9} - \frac{x ^{7}}{7})

\frac{\partial}{\partial x} (\frac{y}{x ^{2} + y ^{2}})

x \to 0 lim (x^{6} cos (\frac{2}{x}))

x \to 0 lim (2 x + 2)

x \to 1 lim (\frac{e ^{x^{2} - 1}}{x ^{2} - 3 x + 2})

What is (\partial)/(\partial x)(e^{xyz-6}) ?
The answer to (\partial)/(\partial x)(e^{xyz-6}) is e^{xyz-6}yz