Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = arcsin(x − y), x = s2 + t2, y = 4 − 6st ∂z ∂s

Given, z=arcsin(x-y),x=s^2+t^2,y=4-6st As per the chain rule of partial differentiation, we have (delz)/(dels)=(delz)/(delx) cdot (delx)/(dels)+(delz)/(dely)cdot(dely)/(dels) ......... equation (1)

Resuelto Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z

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Pregunta: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = arcsin(x − y), x = s2 + t2, y = 4 − 6st ∂z ∂s
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.

z = arcsin(x − y), x = s² + t², y = 4 − 6st

∂z

∂s

=

∂z

∂t

=
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Solución
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For the first step, you need to compute the partial derivatives of which are and , by taking the derivative of arcsin(x-y) with respect to x and y respectively.
Paso 1
Given, $z = \arcsin (x - y), x = s^{2} + t^{2}, y = 4 - 6 s t$
As per the chain rule of partial differentiation, we have
$\frac{\partial z}{\partial s} = \frac{\partial z}{\partial x} \cdot \frac{\partial x}{\partial s} + \frac{\partial z}{\partial y} \cdot \frac{\partial y}{\partial s}$ ......... equation (1)
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Paso 2
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Paso 3
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Paso 4
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Respuesta
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Pregunta: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = arcsin(x − y), x = s2 + t2, y = 4 − 6st ∂z ∂s

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