Question

if f(x,y)=2x^4y^3-xy^2+3y+1 then df/dx is

Answer 1

this is partial derivative wherein we treat the other variable a Constant... therefore
if y variable will be treated as constant... how will you differentiate the function to x?

Answer 2

@Orion1213 i dont get it stilll

Answer 3

in finding derivatives we have the following rules:
(1) d[k]/dx = 0, zero for any constant
(2) d[k f(x)]/dx = k d[f(x)]/dx, constant k is unchanged when differentiated with a variable or a function of x
(3) d[x^n] = nx^(n-1) dx, power formula

Answer 4

1st term: 2x^4y^3, since we'll be finding the derivative to x, we'll treat y as a constant same as 2, applying rule (2), and for x^4 we use rule (3)...

Answer 5

... same with remaining terms... combining all terms as per operation involve in original function to complete the partial differentiation with d f(x,y)/dx...

Answer 6

so the answer must be 8 x^3 y^3 - y^2 ??

Answer 7

Correct!

Answer 8

yup...