Find the first partial derivatives of the following function. f(x,y)=3x2+8xy+y2

Question

Find the first partial derivatives of the following function.  f(x,y)=3x2+8xy+y2

saiyansruleA · Accepted Answer

Step 1  To calculate the first partial derivatives of the given function of two variables  Step 2  Partial derivative with respect to the variable x is found by treating the variable y as constant and applying the standared methods of differentiating a function of one variable (x). Similarly , for partial differentiation with respec to y.  Step 3  Partial derivative of f (x,y) with respect to x  f(x,y)=3x2+8xy+y2  f(x,y)=(3x2+8xy+y2)12  Partial differentiation wrt x; y=constant  ∂f∂x=12(3x2+8xy+y2)12−1×(6x+8y)   (chain rule)  =3x+4y3x2+8xy+y2  Step 4  Partial derivative with respect to y  f(x,y)=3x2+8xy+y2  f(x,y)=(3x2+8xy+y2)12  Partial differentiation wrt y; x=constant  ∂f∂y=12(3x2+8xy+y2)12−1×(8x+2y)   (chain rule)  =4x+y3x2+8xy+y2  Step 5  ANSWER:  ∂f∂x=3x+4y3x2+8xy+y2  ∂f∂y=4x+y3x2+8xy+y2

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Find the first partial derivatives of the following function. f(x,y)=\sqr

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