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

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

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(\partial)/(\partial x)(e^{x+y+z})

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

e^{x + y + z}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + y + z) = 1

= e^{x + y + z} \cdot 1

Simplify

= e^{x + y + z}

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

\frac{d}{d x} (- 6 e^{- 3 x^{2}} x)

\frac{d y}{d x} = 9 x + y, y (0) = 9

6 tan (x), at x = \frac{π}{3}

y = \frac{6 x ^{2} + 8 x + 8}{x}

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