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

The derivative of ln(3x+2x^2) is (3+4x)/(3x+2x^2)

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

The first derivative of ln(3x+2x^2) is (3+4x)/(3x+2x^2)

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

\frac{3 + 4 x}{3 x + 2 x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x + 2 x^{2}) = 3 + 4 x

= \frac{1}{3 x + 2 x ^{2}} (3 + 4 x)

Simplify

\frac{1}{3 x + 2 x ^{2}} (3 + 4 x) : \frac{3 + 4 x}{3 x + 2 x ^{2}}

= \frac{3 + 4 x}{3 x + 2 x ^{2}}

\frac{d}{d x} (7 e^{x} csc (x))

x \to 7.6 lim (8.6 x + 1.8)

f (x) = - x^{2} - 4 x + 4, at x = - 2

\frac{1 - 3 x + x ^{3}}{x ^{3}}

\frac{d}{d x} (sin (x y))

What is the derivative of ln(3x+2x^2) ?
The derivative of ln(3x+2x^2) is (3+4x)/(3x+2x^2)
What is the first derivative of ln(3x+2x^2) ?
The first derivative of ln(3x+2x^2) is (3+4x)/(3x+2x^2)