What is derivative of y(X)=(5X^3+2X^2-1)/(X^2) ?

The answer to derivative of y(X)=(5X^3+2X^2-1)/(X^2) is (dy)/(dx)=(5x^3+2-x^3y)/(x^4)

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derivative of y(X)=(5X^3+2X^2-1)/(X^2)

derivative of

y = \frac{5 x ^{3} + 2 x ^{2} - 1}{x ^{2}}

\frac{d y}{d x} = \frac{5 x ^{3} + 2 - x ^{3} y}{x ^{4}}

Solution steps

y x = \frac{5 x ^{3} + 2 x ^{2} - 1}{x ^{2}}

Treat

y

y (x)

Differentiate both sides:

x \frac{d y}{d x} + y = \frac{5 x ^{3} + 2}{x ^{3}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{5 x ^{3} + 2 - x ^{3} y}{x ^{4}}

\frac{d y}{d x} = \frac{5 x ^{3} + 2 - x ^{3} y}{x ^{4}}

What is derivative of y(X)=(5X^3+2X^2-1)/(X^2) ?
The answer to derivative of y(X)=(5X^3+2X^2-1)/(X^2) is (dy)/(dx)=(5x^3+2-x^3y)/(x^4)