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

The derivative of ((x^2+1/(2x+1))^2) is (2(x^2+1)(2x^2+2x-2))/((2x+1)^3)

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

The first derivative of ((x^2+1/(2x+1))^2) is (2(x^2+1)(2x^2+2x-2))/((2x+1)^3)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = 15 - \frac{3 y}{290}

x \to 0 lim (sin (\frac{4}{x}))

\frac{d y}{d x} = x y + \frac{x}{y}

\int (x^{e} + e^{x}) d x

\frac{\partial}{\partial x} ((4 x + 6 y)^{4})

What is the derivative of ((x^2+1/(2x+1))^2) ?
The derivative of ((x^2+1/(2x+1))^2) is (2(x^2+1)(2x^2+2x-2))/((2x+1)^3)
What is the first derivative of ((x^2+1/(2x+1))^2) ?
The first derivative of ((x^2+1/(2x+1))^2) is (2(x^2+1)(2x^2+2x-2))/((2x+1)^3)