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} (\frac{3}{4 x})

\int_{0}^{\frac{π}{4}} 8 sec^{2} (x) d x

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

f (x) = cos (2) (x)

\int \frac{1}{25 - 9 x ^{2}} 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)