What is (\partial)/(\partial x)(x^2(e^{-xyz})) ?

The answer to (\partial)/(\partial x)(x^2(e^{-xyz})) is 2e^{-xyz}x-e^{-xyz}x^2yz

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(\partial)/(\partial x)(x^2(e^{-xyz}))

\frac{\partial}{\partial x} (x^{2} (e^{- x yz}))

2 e^{- x yz} x - e^{- x yz} x^{2} yz

Solution steps

\frac{\partial}{\partial x} (x^{2} (e^{- x yz}))

Treat

y, z

as constants

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{- x yz}

= \frac{\partial}{\partial x} (x^{2}) e^{- x yz} + \frac{\partial}{\partial x} (e^{- x yz}) x^{2}

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

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

= 2 x e^{- x yz} + (- yz e^{- yz x}) x^{2}

Simplify

= 2 e^{- x yz} x - e^{- x yz} x^{2} yz

\frac{d}{d x} ((2 x + 1) (x - 5))

\int \frac{21 π}{2} cos (\frac{21 π x}{2}) d x

\frac{d}{d x} (x + 2 \cdot sin (x))

x \to 0 lim (\frac{8}{2 + e ^{\frac{1}{x}}})

\frac{d}{d x} (\frac{2 cos ( x )}{1 + sin ( x )})

What is (\partial)/(\partial x)(x^2(e^{-xyz})) ?
The answer to (\partial)/(\partial x)(x^2(e^{-xyz})) is 2e^{-xyz}x-e^{-xyz}x^2yz