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

The derivative of (2-x/(1+2x^2)) is (2x^2-8x-1)/((1+2x^2)^2)

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

The first derivative of (2-x/(1+2x^2)) is (2x^2-8x-1)/((1+2x^2)^2)

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

\frac{2 x ^{2} - 8 x - 1}{( 1 + 2 x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (1 + 2 x^{2}) = 4 x

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

Simplify

\frac{( - 1 ) ( 1 + 2 x ^{2} ) - 4 x ( 2 - x )}{( 1 + 2 x ^{2} ) ^{2}} : \frac{2 x ^{2} - 8 x - 1}{( 1 + 2 x ^{2} ) ^{2}}

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

x \to 0 lim (16 - 7 x)

\int - cos (x) + C d x

\frac{d}{d t} (4 e^{- t})

4 x^{2} - 2

\frac{d}{d x} (3 4 - \frac{1}{2} x)

What is the derivative of (2-x/(1+2x^2)) ?
The derivative of (2-x/(1+2x^2)) is (2x^2-8x-1)/((1+2x^2)^2)
What is the first derivative of (2-x/(1+2x^2)) ?
The first derivative of (2-x/(1+2x^2)) is (2x^2-8x-1)/((1+2x^2)^2)