What is the derivative of (x^2/(1+6x)) ?

The derivative of (x^2/(1+6x)) is (2x+6x^2)/((1+6x)^2)

What is the first derivative of (x^2/(1+6x)) ?

The first derivative of (x^2/(1+6x)) is (2x+6x^2)/((1+6x)^2)

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\frac{d}{d x} (\frac{x ^{2}}{1 + 6 x})

\frac{2 x + 6 x ^{2}}{( 1 + 6 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{1 + 6 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 1 + 6 x ) - \frac{d}{d x} ( 1 + 6 x ) x ^{2}}{( 1 + 6 x ) ^{2}}

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

\frac{d}{d x} (1 + 6 x) = 6

= \frac{2 x ( 1 + 6 x ) - 6 x ^{2}}{( 1 + 6 x ) ^{2}}

Expand

2 x (1 + 6 x) - 6 x^{2} : 2 x + 6 x^{2}

= \frac{2 x + 6 x ^{2}}{( 1 + 6 x ) ^{2}}

\frac{d}{d x} (\frac{3 x ^{2}}{1 + 2 x})

\frac{d}{d x} (- 4 tan (x) - csc (x))

\int_{0}^{1} 3 (1 + x)^{6} d x

\int r 4 - r^{2} - r^{2} d r

\frac{1}{( s )}

What is the derivative of (x^2/(1+6x)) ?
The derivative of (x^2/(1+6x)) is (2x+6x^2)/((1+6x)^2)
What is the first derivative of (x^2/(1+6x)) ?
The first derivative of (x^2/(1+6x)) is (2x+6x^2)/((1+6x)^2)