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

The derivative of (2x^2/(x-3)) is (2(x^2-6x))/((x-3)^2)

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

The first derivative of (2x^2/(x-3)) is (2(x^2-6x))/((x-3)^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 3) = 1

= 2 \cdot \frac{2 x ( x - 3 ) - 1 \cdot x ^{2}}{( x - 3 ) ^{2}}

Simplify

2 \cdot \frac{2 x ( x - 3 ) - 1 \cdot x ^{2}}{( x - 3 ) ^{2}} : \frac{2 ( x ^{2} - 6 x )}{( x - 3 ) ^{2}}

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

\int \frac{1}{x ^{1.4}} d x

\int \frac{y ^{2} + 26 y + 169}{( y ^{2} + 169 ) ^{2}} d y

\int (cos (2 x) + sin (2 x))^{2} d x

(ln (y))^{7} \frac{d y}{d x} = x^{7} y, y (1) = e^{2}

\frac{( x ^{3} - 5 x + 186 )}{x ^{2} - x - 42}

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