So here we are given a real, valued function, which is represented by f by the 2 real variable, which is defined as f of x y. That will be equals to 2 of i raise to the power 3 divided by the x square plus y square, where we can say that x of y is not equal to 00 and we can say that f of 00 point that will be equals to 0. So now we can say that value of f, divided by the gale of x will be equal to limit. That is approaching towards 0 f of x, plus y h of y minus f of x y, which is divided by the h. So this will be equals to limit, is approaching towards 02 y raised to the power 3 divided by the x plus h. Whole square plus y square. Minus 2 y, raised to the power 3 divided by the x, raised to the power 2 plus y, raise to the power 2, which is further divided by the h. So from here we can say that limit h is approaching towards 0 will be 2 of y raised to the power 31 divided by the x plus h, whole square plus y square minus 1, divided by the x square plus y square, which is further divided by The h, so this function will be equals to limit, which is h, is approaching towards 0. So 2 of y raised to the power 3 x, squared plus y square minus x square, minus 2 of x, h, minus x square minus y square, which is de divided by x square plus y square x, plus h, whole square plus y square. So this will be equals to limit is approaching towards 02 of y raised to the power 3 minus 2 of x, h, minus h, squared divided by the h, multiplied by the x square plus y square, multiplied by the x plus h, whole square plus y square. So this term will be 0 divided by the 0 type. So from here we can write it as 2 y cube, divided by the x square plus y squared limit of his approaching towards 0 minus 2 of x, minus 2 of h, divided by the x plus h, whole square plus y square plus h of 2 x, Plus 2 of h, an by applying here al hospital rule, we get the function as 2 of y raised to the power 3 plugging into the value. So we have applied here y hospital rule,…