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Функціональний калькулятор градієнта

Крок за кроком знайдіть градієнт функції

Калькулятор знайде градієнт заданої функції (в заданій точці, якщо потрібно), з показаними кроками.

Enter a function:
Enter the order of variables and/or a point:
If you don't need the order of variables, leave it empty.
If you want a specific order of variables, enter variables comma-separated, like .
If you want the gradient at a specific point, for example, at , enter it as , or simply if you want the order of variables to be detected automatically.

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Solution

Your input: find the gradient of f=x3+y5at (x,y)=(1,7)

To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.

f=(fx,fy)

fx=3x2 (for steps, see derivative calculator)

fy=5y4 (for steps, see derivative calculator)

Finally, plug in the point:

f(1,7)=(3,12005)

Answer

(x3+y5)(x,y)=(3x2,5y4)

(x3+y5)|(x,y)=(1,7)=(3,12005)