What is the derivative of (4x^2+72x)/(x-2) ?

The derivative of (4x^2+72x)/(x-2) is (4x^2-16x-144)/((x-2)^2)

What is the first derivative of (4x^2+72x)/(x-2) ?

The first derivative of (4x^2+72x)/(x-2) is (4x^2-16x-144)/((x-2)^2)

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derivative of

\frac{4 x ^{2} + 72 x}{x - 2}

\frac{4 x ^{2} - 16 x - 144}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} + 72 x}{x - 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} + 72 x ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( 4 x ^{2} + 72 x )}{( x - 2 ) ^{2}}

\frac{d}{d x} (4 x^{2} + 72 x) = 8 x + 72

\frac{d}{d x} (x - 2) = 1

= \frac{( 8 x + 72 ) ( x - 2 ) - 1 \cdot ( 4 x ^{2} + 72 x )}{( x - 2 ) ^{2}}

Simplify

\frac{( 8 x + 72 ) ( x - 2 ) - 1 \cdot ( 4 x ^{2} + 72 x )}{( x - 2 ) ^{2}} : \frac{4 x ^{2} - 16 x - 144}{( x - 2 ) ^{2}}

= \frac{4 x ^{2} - 16 x - 144}{( x - 2 ) ^{2}}

\int π sin (π) θ d θ

x \to 0 lim ((tan (4 x))^{x})

y^{^{''}} + 4 y^{^{'}} + 7 y = 0

\frac{\partial}{\partial x} (x ln (y + x))

y^{^{'}} = e (- 2 t) - y

What is the derivative of (4x^2+72x)/(x-2) ?
The derivative of (4x^2+72x)/(x-2) is (4x^2-16x-144)/((x-2)^2)
What is the first derivative of (4x^2+72x)/(x-2) ?
The first derivative of (4x^2+72x)/(x-2) is (4x^2-16x-144)/((x-2)^2)