If u=e^(xyz) find (del^(3)u)/(del x del y del z)

Differentiate u: Differentiate u with respect to x. We have u = e^(xyz). The first partial derivative of u with respect to x is found by treating y and z as constants and differentiating e^(xyz) with respect to x. du/dx = yz * e^(xyz) Differentiate du/dx: Differentiate the result from Step 1 with respect to y. Now we take the partial derivative of du/dx with respect to y, treating x and z as constants. d^2u/(dx dy) = z * e^(xyz) Differentiate d^2u/(dx dy): Differentiate the result from Step 2 with respect to z. Finally, we take the partial derivative of d^2u/(dx dy) with respect to z, treating x and y as constants. d^3u/(dx dy dz) = e^(xyz)

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If $u=e^{xyz}$ find $\frac{\partial^{3}u}{\partial x \partial y \partial z}$

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Algebra 2

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Q. If

u=e^{xyz}

find

\frac{\partial^{3}u}{\partial x \partial y \partial z}

Differentiate $u$ : Differentiate $u$ with respect to $x$ . We have $u = e^{xyz}$ . The first partial derivative of $u$ with respect to $x$ is found by treating $y$ and $z$ as constants and differentiating $e^{xyz}$ with respect to $x$ . $u$ $0$
Differentiate $\frac{du}{dx}$ : Differentiate the result from Step $1$ with respect to $y$ . Now we take the partial derivative of $\frac{du}{dx}$ with respect to $y$ , treating $x$ and $z$ as constants. $\frac{d^2u}{dx dy} = z \cdot e^{xyz}$
Differentiate $\frac{d^2u}{dx dy}$ : Differentiate the result from Step $2$ with respect to $z$ . Finally, we take the partial derivative of $\frac{d^2u}{dx dy}$ with respect to $z$ , treating $x$ and $y$ as constants. $\frac{d^3u}{dx dy dz} = e^{xyz}$