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

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

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

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

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derivative of

\frac{x ^{2}}{1 + 2 x}

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

Solution steps

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

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

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

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

Expand

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

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

(6 y + 2 x - 7) d x + (8 y + 6 x - 1) d y = 0

x \to + 3 lim (\frac{6 x}{x - 3})

e^{x^{2}}

\int 2 sin (5 x) d x

e^{t} cos (5 t)

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