$$
f(x, y)=\frac{y^{2}}{x}
$$

What is the partial derivative of $f$ with respect to $x$ ?
Choose 1 answer:
(A) $\frac{-y^{2}}{x^{2}}$
(B) $\frac{2 y}{x}$
(C) $\frac{-2 y}{x^{2}}$
(D) $\frac{2 y x-y^{2}}{x^{2}}$

Question

$$
f(x, y)=\frac{y^{2}}{x}
$$

What is the partial derivative of $f$ with respect to $x$ ?
Choose 1 answer:
(A) $\frac{-y^{2}}{x^{2}}$
(B) $\frac{2 y}{x}$
(C) $\frac{-2 y}{x^{2}}$
(D) $\frac{2 y x-y^{2}}{x^{2}}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ asksia-ll calculator input: Y²%2Fx+differentiate+with+respect+to+x ‖ ‖ step 2 ⋮ answer with steps: $d/dx(Y^2/x) = -Y^2/x^2$ ‖ ‖ step 3 ⋮ x!=0, Y = 0 ‖ ‖ step 4 ⋮ ${x \in \mathbb{R} : x eq 0}$ ‖ ‖ step 5 ⋮ ${y \in \mathbb{R} : (y = 0 ext{ and } Y = 0) ext{ or } (y < 0 ext{ and } Y eq 0)}$ ‖ ‖ step 6 ⋮ even ‖ ***A*** ∻Key Concept∻ ⚹Partial Derivative with respect to x⚹ ∻Explanation∻ ⚹The partial derivative of $f(x, y) = \frac{y^2}{x}$ with respect to $x$ is computed by treating $y$ as a constant and differentiating $y^2/x$ with respect to $x$, which results in $-\frac{y^2}{x^2}$.◊What is the formula for calculating the partial derivative of a function with respect to a specific variable in multivariable calculus?⍭ Generate me a similar question◊⚹

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