What is the derivative of (y^2-3x^2/(y^4)) ?

The derivative of (y^2-3x^2/(y^4)) is (2(6x^2\frac{dy)/(dx)-3xy-(dy)/(dx)y^2)}{y^5}

What is the first derivative of (y^2-3x^2/(y^4)) ?

The first derivative of (y^2-3x^2/(y^4)) is (2(6x^2\frac{dy)/(dx)-3xy-(dy)/(dx)y^2)}{y^5}

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\frac{d}{d x} (\frac{y ^{2} - 3 x ^{2}}{y ^{4}})

\frac{2 ( 6 x ^{2} \frac{d y}{d x} - 3 x y - \frac{d y}{d x} y ^{2} )}{y ^{5}}

Solution steps

\frac{d}{d x} (\frac{y ^{2} - 3 x ^{2}}{y ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( y ^{2} - 3 x ^{2} ) y ^{4} - \frac{d}{d x} ( y ^{4} ) ( y ^{2} - 3 x ^{2} )}{( y ^{4} ) ^{2}}

\frac{d}{d x} (y^{2} - 3 x^{2}) = 2 y \frac{d y}{d x} - 6 x

\frac{d}{d x} (y^{4}) = 4 y^{3} \frac{d y}{d x}

= \frac{( 2 y \frac{d y}{d x} - 6 x ) y ^{4} - 4 y ^{3} \frac{d y}{d x} ( y ^{2} - 3 x ^{2} )}{( y ^{4} ) ^{2}}

Simplify

\frac{( 2 y \frac{d y}{d x} - 6 x ) y ^{4} - 4 y ^{3} \frac{d y}{d x} ( y ^{2} - 3 x ^{2} )}{( y ^{4} ) ^{2}} : \frac{2 ( 6 x ^{2} \frac{d y}{d x} - 3 x y - \frac{d y}{d x} y ^{2} )}{y ^{5}}

= \frac{2 ( 6 x ^{2} \frac{d y}{d x} - 3 x y - \frac{d y}{d x} y ^{2} )}{y ^{5}}

\frac{\partial}{\partial x} (+ 6 - 5 + 6 x)

n = 0 \sum \infty \frac{2}{7 ^{n}}

x \to 2 - lim (arcsin (x - 1))

x \to π lim (\frac{1}{x - π})

What is the derivative of (y^2-3x^2/(y^4)) ?
The derivative of (y^2-3x^2/(y^4)) is (2(6x^2\frac{dy)/(dx)-3xy-(dy)/(dx)y^2)}{y^5}
What is the first derivative of (y^2-3x^2/(y^4)) ?
The first derivative of (y^2-3x^2/(y^4)) is (2(6x^2\frac{dy)/(dx)-3xy-(dy)/(dx)y^2)}{y^5}