What is the derivative of ln(x^2(3x^2+6)) ?

The derivative of ln(x^2(3x^2+6)) is (2(3x^2+6))/x+12xln(x)

What is the first derivative of ln(x^2(3x^2+6)) ?

The first derivative of ln(x^2(3x^2+6)) is (2(3x^2+6))/x+12xln(x)

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\frac{d}{d x} (ln (x^{2}) (3 x^{2} + 6))

\frac{2 ( 3 x ^{2} + 6 )}{x} + 12 x ln (x)

Solution steps

\frac{d}{d x} (ln (x^{2}) (3 x^{2} + 6))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x^{2}), g = 3 x^{2} + 6

= \frac{d}{d x} (ln (x^{2})) (3 x^{2} + 6) + \frac{d}{d x} (3 x^{2} + 6) ln (x^{2})

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

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

= \frac{2}{x} (3 x^{2} + 6) + 6 x ln (x^{2})

Simplify

\frac{2}{x} (3 x^{2} + 6) + 6 x ln (x^{2}) : \frac{2 ( 3 x ^{2} + 6 )}{x} + 12 x ln (x)

= \frac{2 ( 3 x ^{2} + 6 )}{x} + 12 x ln (x)

\int_{2}^{5} (- 3 v + 4) d v

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

\int 10 x sec^{2} (x) d x

x \to - 6 lim (\frac{x ^{2} - 1}{6 - x})

\frac{d}{d x} (\frac{e ^{3 x^{2}}}{5 x})

What is the derivative of ln(x^2(3x^2+6)) ?
The derivative of ln(x^2(3x^2+6)) is (2(3x^2+6))/x+12xln(x)
What is the first derivative of ln(x^2(3x^2+6)) ?
The first derivative of ln(x^2(3x^2+6)) is (2(3x^2+6))/x+12xln(x)