"Compute the derivatives indicated. f(x,y)=3x2y−6xy4,∂2f∂x2 and ∂2f∂y2" was answered by students like you

College
Calculus and Analysis
Differential Calculus
Derivatives

beljuA

Answered question

2021-10-01

Compute the derivatives indicated.

f (x, y) = 3 x^{2} y - 6 x y^{4}, \frac{\partial^{2} f}{\partial x^{2}} and \frac{\partial^{2} f}{\partial y^{2}}

Answer & Explanation

Sadie Eaton

Skilled2021-10-02Added 104 answers

Step 1
Here given as
$f (x, y) = 3 x^{2} y - 6 x y^{4}$
Now
$\frac{\partial f}{\partial x} = \frac{\partial}{\partial x} (3 x^{2} y - 6 x y^{4})$
$= (6 x y - 6 y^{4})$
$\frac{\partial^{2} f}{\partial x^{2}} = \frac{\partial}{\partial x} (6 x y - 6 y^{4})$
$\Rightarrow \frac{\partial^{2} f}{\partial x^{2}} = 6 y$
Step 2
Thus
$\frac{\partial f}{\partial y} = \frac{\partial}{\partial y} (3 x^{2} y - 6 x y^{4})$
$= (3 x^{2} - 24 x y^{3})$
$\frac{\partial^{2} f}{\partial y^{2}} = \frac{\partial}{\partial y} (3 x^{2} - 24 x y^{3})$
$\Rightarrow \frac{\partial^{2} f}{\partial y^{2}} - 62 x y^{2}$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?