What is the derivative of 2ln(3x^2-1) ?

The derivative of 2ln(3x^2-1) is (12x)/(3x^2-1)

What is the first derivative of 2ln(3x^2-1) ?

The first derivative of 2ln(3x^2-1) is (12x)/(3x^2-1)

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

\frac{12 x}{3 x ^{2} - 1}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - 1) = 6 x

= 2 \cdot \frac{1}{3 x ^{2} - 1} \cdot 6 x

Simplify

2 \cdot \frac{1}{3 x ^{2} - 1} \cdot 6 x : \frac{12 x}{3 x ^{2} - 1}

= \frac{12 x}{3 x ^{2} - 1}

\frac{d}{d x} (- 19 x^{2} + 4 x + 22)

g (x) = x^{5} - 2 x

\int \frac{1}{x ^{2} - x + 6} d x

\int e^{- x y} d y

\int (csc (x))^{2} d x

What is the derivative of 2ln(3x^2-1) ?
The derivative of 2ln(3x^2-1) is (12x)/(3x^2-1)
What is the first derivative of 2ln(3x^2-1) ?
The first derivative of 2ln(3x^2-1) is (12x)/(3x^2-1)