What is the derivative of f(x)= 4/(1-2x^2) ?

The derivative of f(x)= 4/(1-2x^2) is (16x)/((1-2x^2)^2)

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

The first derivative of f(x)= 4/(1-2x^2) is (16x)/((1-2x^2)^2)

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derivative of

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

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

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})^{- 1})

Apply the chain rule:

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

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

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

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

Simplify

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

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

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