Question

find the partial derivative of 2xy w.r.t x​

Answer 1

Answer:

using product rule we can derivate the function

1. y=d(2xy)/dy
2. differentiating both sides w.r.t to x
3. dy/dx=2y(dx/dx) +x (dy/ dx)
4. dy/dx=2y(1) +x dy/dx
5. dy/dx-xdy/dx=2y
6. dy/ dx(1- x) =2y
7. dy/dx= 2y/(1-x)

Answer 2

The partial derivative of 2xy w.r.t. 'x' is equal to 2y.

→ To calculate the partial derivative of a function with respect to a variable, we differentiate the function treating all the other variables as a constant.

→ Hence while calculating the partial derivative of 2xy w.r.t. 'x' we will differentiate 2xy w.r.t. 'x' treating y as a constant:

                                          $=\frac{d(2xy)}{dx}|_{y=constant} \\\\=2y\frac{dx}{dx} |_{y=constant} \\\\=2y$

→The partial derivative of 2xy w.r.t. 'x' comes out to be equal to 2y.

Hence, the partial derivative of 2xy w.r.t. 'x' is equal to 2y.

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