Question

if (z)=(x^(2)+y^(2))/sqrt((x+y)) prove that x(del z)/(del x)+y*(del z)/(del x)+y*(del z)/(del x)=(3)/(2)x
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Answer 1

Step-by-step explanation:

Since you're dealing with a multivariable function, you must treat x, y, and z as independent variables and calculate the partial derivative of w, your dependent variable, with respect to x, y, and z.

When you differentiate with respect to x, you treat y and z as constants. LIkewise, when you differentiate with respect to y, you treat x and z as constants, and so on.

So, let's first differentiate w with respect to x

∂w∂x=∂∂x√x2+y2+z2

∂w∂x=12⋅(x2+y2+z2)−12⋅∂∂x(x2+y2+z2)

∂w∂x=12⋅1√x2+y2+z2⋅(2x+0+0)

∂w