What is the derivative of ((6x^2+4)/((3y^2-4))) ?

The derivative of ((6x^2+4)/((3y^2-4))) is (12x(3y^2-4)-6y\frac{dy)/(dx)(6x^2+4)}{(3y^2-4)^2}

What is the first derivative of ((6x^2+4)/((3y^2-4))) ?

The first derivative of ((6x^2+4)/((3y^2-4))) is (12x(3y^2-4)-6y\frac{dy)/(dx)(6x^2+4)}{(3y^2-4)^2}

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

\frac{12 x ( 3 y ^{2} - 4 ) - 6 y \frac{d y}{d x} ( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (6 x^{2} + 4) = 12 x

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

= \frac{12 x ( 3 y ^{2} - 4 ) - 6 y \frac{d y}{d x} ( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 ) ^{2}}

\int_{- 3}^{0} 1 + 9 - x^{2} d x

\frac{200}{( s + 10 ) ( s + 100 )}

x^{^{''}} - x = 0

\frac{d}{d x} (x^{3} - 2 x^{2} + x - 20)

\int_{0}^{1} x sin (nπ x) d x

What is the derivative of ((6x^2+4)/((3y^2-4))) ?
The derivative of ((6x^2+4)/((3y^2-4))) is (12x(3y^2-4)-6y\frac{dy)/(dx)(6x^2+4)}{(3y^2-4)^2}
What is the first derivative of ((6x^2+4)/((3y^2-4))) ?
The first derivative of ((6x^2+4)/((3y^2-4))) is (12x(3y^2-4)-6y\frac{dy)/(dx)(6x^2+4)}{(3y^2-4)^2}