What is the derivative of 5/(1-4x^2) ?

The derivative of 5/(1-4x^2) is (40x)/((1-4x^2)^2)

What is the first derivative of 5/(1-4x^2) ?

The first derivative of 5/(1-4x^2) is (40x)/((1-4x^2)^2)

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\frac{d}{d x} (\frac{5}{1 - 4 x ^{2}})

\frac{40 x}{( 1 - 4 x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5}{1 - 4 x ^{2}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{1 - 4 x ^{2}})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((1 - 4 x^{2})^{- 1})

Apply the chain rule:

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

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

\frac{d}{d x} (1 - 4 x^{2}) = - 8 x

= 5 (- \frac{1}{( 1 - 4 x ^{2} ) ^{2}} (- 8 x))

Simplify

5 (- \frac{1}{( 1 - 4 x ^{2} ) ^{2}} (- 8 x)) : \frac{40 x}{( 1 - 4 x ^{2} ) ^{2}}

= \frac{40 x}{( 1 - 4 x ^{2} ) ^{2}}

\frac{x + 2}{x ^{3} + x - 6}

\frac{d}{d x} (\frac{x}{x ^{2} + 196})

x \to 14 lim (x + 2)

g (x) = ln (x e^{- 9 x})

4 x + 12, x^{2}

What is the derivative of 5/(1-4x^2) ?
The derivative of 5/(1-4x^2) is (40x)/((1-4x^2)^2)
What is the first derivative of 5/(1-4x^2) ?
The first derivative of 5/(1-4x^2) is (40x)/((1-4x^2)^2)