If $x=r sin \theta cos \varphi$, $y=r sin\theta\varphi$, $ z=r cos\theta$, then find $[ \dfrac {\partial (r, \theta , \varphi)}{\partial (x,y,z) } ]$

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$x=r sin \theta cos \varphi$ ,

$y=r sin\theta\varphi$ ,

$z=r cos\theta$ , then find

$[ \dfrac {\partial (r, \theta , \varphi)}{\partial (x,y,z) } ]$

written 3.9 years ago by

teamques10 ★ 69k

modified 3.0 years ago by

yashbeer ★ 11k

engineering mathematics

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written 3.9 years ago by

teamques10 ★ 69k

$x = r sin \theta cos \phi \; y = r sin \theta sin \phi \; and z= r cos \theta \\ \text{ According to the definition,} \\ {\delta (x,y,z) \over \delta (r, \theta, \phi)} = \begin{vmatrix} {\delta x \over \delta r} & {\delta x \over \delta \theta} & {\delta …

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