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abondantQ

Answered question

2021-10-12

Find all second-order partial derivatives for the following.

z = 7 y e^{6 x}

Answer & Explanation

curwyrm

Skilled2021-10-13Added 87 answers

Step 1
Given that

z = 7 y e^{6 x}

.
Obtain first partial derivative.

\frac{\partial z}{\partial x} = {(7 y e^{6 x})}^{'}

= 42 y e^{6 x}

\frac{\partial z}{\partial y} = {(7 y e^{6 x})}^{'}

= 7 e^{6 x}

Step 2
Obtain second partial derivative.

\frac{\partial^{2} z}{\partial x^{2}} = (7 y e^{6 x})^{″}

= {(42 y e^{6 x})}^{'}

= 252 y e^{6 x}

\frac{\partial^{2} z}{\partial x \partial y} = (7 y e^{6 x})^{″}

= {(42 y e^{6 x})}^{'}

= 42 e^{6 x}

\frac{\partial^{2} z}{\partial y^{2}} = (7 y e^{6 x})^{″}

=0

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