Question

Find the partial derivatives fx and fy of the function f(x,y). The variables are restricted to a domain on which the function is defined.f(x,y)= 13x^2y³ 4xy^2 – 6x^2.fx(x,y)=fy(x,y)=

Answer 1

To find the partial derivatives fx and fy of the function f(x,y)= 13x²y³ + 4xy² - 6x³, we differentiate the function with respect to x and y, respectively. The partial derivative fx(x,y) is 26xy³ - 12x, and the partial derivative fy(x,y) is 26x²y² + 8y.

Step-by-step explanation:

To find the partial derivatives fx and fy of the function f(x,y), we differentiate the function with respect to x and y, respectively. Taking the derivative of 13x²y³, we get 26xy³. Taking the derivative of 4xy², we get 4y². Taking the derivative of -6x², we get -12x.

Therefore, the partial derivative fx(x,y) is 26xy³ - 12x, and the partial derivative fy(x,y) is 26x²y² + 8y.