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

The derivative of 4/((1+2x^2)) is -(16)/((1+2x)^3)

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

The first derivative of 4/((1+2x^2)) is -(16)/((1+2x)^3)

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

- \frac{16}{( 1 + 2 x ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= 4 (- \frac{2}{( 1 + 2 x ) ^{3}} \cdot 2)

Simplify

4 (- \frac{2}{( 1 + 2 x ) ^{3}} \cdot 2) : - \frac{16}{( 1 + 2 x ) ^{3}}

= - \frac{16}{( 1 + 2 x ) ^{3}}

\frac{d}{d x} (ln (17 x))

x \to - 5 lim (3 x - ∣ x + 5 ∣)

y = \frac{1}{x - 2}, at x = 5

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

\int (1 - x)^{n} d x

What is the derivative of 4/((1+2x^2)) ?
The derivative of 4/((1+2x^2)) is -(16)/((1+2x)^3)
What is the first derivative of 4/((1+2x^2)) ?
The first derivative of 4/((1+2x^2)) is -(16)/((1+2x)^3)