What is the derivative of (7x^3y/(x-4y)) ?

The derivative of (7x^3y/(x-4y)) is (7(x^4\frac{dy)/(dx)+2x^3y-12x^2y^2)}{(x-4y)^2}

What is the first derivative of (7x^3y/(x-4y)) ?

The first derivative of (7x^3y/(x-4y)) is (7(x^4\frac{dy)/(dx)+2x^3y-12x^2y^2)}{(x-4y)^2}

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\frac{d}{d x} (\frac{7 x ^{3} y}{x - 4 y})

\frac{7 ( x ^{4} \frac{d y}{d x} + 2 x ^{3} y - 12 x ^{2} y ^{2} )}{( x - 4 y ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x ^{3} y}{x - 4 y})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{x ^{3} y}{x - 4 y})

Apply the Quotient Rule:

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

= 7 \cdot \frac{\frac{d}{d x} ( x ^{3} y ) ( x - 4 y ) - \frac{d}{d x} ( x - 4 y ) x ^{3} y}{( x - 4 y ) ^{2}}

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

\frac{d}{d x} (x - 4 y) = 1 - 4 \frac{d y}{d x}

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

Simplify

7 \cdot \frac{( 3 x ^{2} y + \frac{d y}{d x} x ^{3} ) ( x - 4 y ) - ( 1 - 4 \frac{d y}{d x} ) x ^{3} y}{( x - 4 y ) ^{2}} : \frac{7 ( x ^{4} \frac{d y}{d x} + 2 x ^{3} y - 12 x ^{2} y ^{2} )}{( x - 4 y ) ^{2}}

= \frac{7 ( x ^{4} \frac{d y}{d x} + 2 x ^{3} y - 12 x ^{2} y ^{2} )}{( x - 4 y ) ^{2}}

What is the derivative of (7x^3y/(x-4y)) ?
The derivative of (7x^3y/(x-4y)) is (7(x^4\frac{dy)/(dx)+2x^3y-12x^2y^2)}{(x-4y)^2}
What is the first derivative of (7x^3y/(x-4y)) ?
The first derivative of (7x^3y/(x-4y)) is (7(x^4\frac{dy)/(dx)+2x^3y-12x^2y^2)}{(x-4y)^2}