find-the-partial-derivatives-of-first-and-second-order-for-the-function-f-x-y-x-3-y-3xy-y-4-

Question Number 88434 by Rio Michael last updated on 10/Apr/20

find the partial derivatives of first and second order

for the function

f (x, y) = x^{3} y + 3 x y + y^{4}

Commented by niroj last updated on 10/Apr/20

f (x, y) = x^{3} y + 3 xy + y^{4}

D . w . r . to x

1^{st} order f (x^{^{'}}) = \frac{df}{dx} = {3 x}^{2} y + 3 y

2^{nd} order f (x^{^{″}}) = \frac{d^{2} f}{{dx}^{2}} = 6 xy .

Again, f (y) = x^{3} y + 3 xy + y^{4}

D . w . r . to y

1^{st} order f (y^{^{'}}) = \frac{df}{dy} = x^{3} + 3 x + {4 y}^{3}

2^{nd} order f (y^{^{″}}) = \frac{d^{2} f}{{dy}^{2}} = {12 y}^{2} .

Commented by Rio Michael last updated on 11/Apr/20

thank you sir