What is the derivative of (y^2-2)/(2y^2) ?

The derivative of (y^2-2)/(2y^2) is 2/(y^3)

What is the first derivative of (y^2-2)/(2y^2) ?

The first derivative of (y^2-2)/(2y^2) is 2/(y^3)

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derivative of

\frac{y ^{2} - 2}{2 y ^{2}}

\frac{2}{y ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

= \frac{1}{2} \cdot \frac{2 y y ^{2} - 2 y ( y ^{2} - 2 )}{( y ^{2} ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{2 y y ^{2} - 2 y ( y ^{2} - 2 )}{( y ^{2} ) ^{2}} : \frac{2}{y ^{3}}

= \frac{2}{y ^{3}}

\int \frac{x ^{3} - 2 x ^{2} + 1}{x - 3} d x

\int_{1}^{2} \frac{( ln ( x ) ) ^{2}}{x} d x

\int_{0}^{\infty} u (t) d t

x \to \infty lim (x \cdot 1)

3^{e^{x}}

What is the derivative of (y^2-2)/(2y^2) ?
The derivative of (y^2-2)/(2y^2) is 2/(y^3)
What is the first derivative of (y^2-2)/(2y^2) ?
The first derivative of (y^2-2)/(2y^2) is 2/(y^3)