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Question Number 53378 by Necxx last updated on 21/Jan/19

i f u = e^{x y z} t h e n u_{x y x} = ?

a) u ({(x y z)}^{2} + 3 x y z + 1) b) u (3 {(x y z)}^{2} + 1)

c) u ({(x y z)}^{2} + 2 y z + 1)

p l e a s e h e l p

Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19

u = e^{x y z}

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

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

= {z e}^{x y z} + y z \times e^{x y z} \times x z

= e^{x y z} (z + {x y z}^{2})

u_{x y z} = e^{x y z} \times \frac{\partial}{\partial z} (z + {x y z}^{2}) + (z + {x y z}^{2}) \times \frac{\partial}{\partial z} (e^{x y z})

= e^{x y z} \times (1 + 2 x y z) + (z + {x y z}^{2}) \times e^{x y z} (x y)

= u [1 + 2 x y z + x y z + x^{2} y^{2} z^{2}]

= u [1 + 3 x y z + x^{2} y^{2} z^{2}] s o o p t i o n a i s c o r r e c t

Commented by Necxx last updated on 21/Jan/19

e x a c t l y \dots . . T h a n k s s o m u c h

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