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Popular >

derivative of y/(x^2)

Solution

\frac{d}{d x} (\frac{y}{x ^{2}})

Solution

\frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{y}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d y}{d x} x ^{2} - \frac{d}{d x} ( x ^{2} ) y}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

= \frac{\frac{d y}{d x} x ^{2} - 2 x y}{( x ^{2} ) ^{2}}

Simplify

\frac{\frac{d y}{d x} x ^{2} - 2 x y}{( x ^{2} ) ^{2}} : \frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

= \frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

Popular Examples

area y=x^2-4,y=0 area

y = x^{2} - 4, y = 0

y^{''}-6y^'-8y=0

y^{^{''}} - 6 y^{^{'}} - 8 y = 0

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\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}))

Frequently Asked Questions (FAQ)

What is the derivative of y/(x^2) ?
The derivative of y/(x^2) is (x\frac{dy)/(dx)-2y}{x^3}
What is the first derivative of y/(x^2) ?
The first derivative of y/(x^2) is (x\frac{dy)/(dx)-2y}{x^3}