What is the derivative of 1/x y ?

The derivative of 1/x y is -y/(x^2)+((dy)/(dx))/x

What is the first derivative of 1/x y ?

The first derivative of 1/x y is -y/(x^2)+((dy)/(dx))/x

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\frac{d}{d x} (\frac{1}{x} y)

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

Solution steps

\frac{d}{d x} (\frac{1}{x} y)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x}, g = y

= \frac{d}{d x} (\frac{1}{x}) y + \frac{d y}{d x} \frac{1}{x}

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= (- \frac{1}{x ^{2}}) y + \frac{d y}{d x} \frac{1}{x}

Simplify

(- \frac{1}{x ^{2}}) y + \frac{d y}{d x} \frac{1}{x} : - \frac{y}{x ^{2}} + \frac{\frac{d y}{d x}}{x}

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

x \to - 3 + lim (\frac{4 x + 3}{x + 3})

\frac{d y}{d x} = 2 x y^{\frac{1}{2}}

4 - x^{2}, 16 - 7 x

\int (9 - x) x d x

What is the derivative of 1/x y ?
The derivative of 1/x y is -y/(x^2)+((dy)/(dx))/x
What is the first derivative of 1/x y ?
The first derivative of 1/x y is -y/(x^2)+((dy)/(dx))/x