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

The derivative of 2/(1+2x) is -4/((1+2x)^2)

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

The first derivative of 2/(1+2x) is -4/((1+2x)^2)

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derivative of

\frac{2}{1 + 2 x}

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{2 + 3 x}{1 + x ^{2}} d x

\int_{1}^{6} x d x

\int_{4}^{8} \frac{x}{x ^{2} - 2 x - 3} d x

f (x) = 2 x + 5 x

f (x) = \frac{1 0 ^{x}}{ln ( 10 )}

What is the derivative of 2/(1+2x) ?
The derivative of 2/(1+2x) is -4/((1+2x)^2)
What is the first derivative of 2/(1+2x) ?
The first derivative of 2/(1+2x) is -4/((1+2x)^2)