What is the derivative of ln(3x^2+4x+5) ?

The derivative of ln(3x^2+4x+5) is (6x+4)/(3x^2+4x+5)

What is the first derivative of ln(3x^2+4x+5) ?

The first derivative of ln(3x^2+4x+5) is (6x+4)/(3x^2+4x+5)

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derivative of

ln (3 x^{2} + 4 x + 5)

\frac{6 x + 4}{3 x ^{2} + 4 x + 5}

Solution steps

\frac{d}{d x} (ln (3 x^{2} + 4 x + 5))

Apply the chain rule:

\frac{1}{3 x ^{2} + 4 x + 5} \frac{d}{d x} (3 x^{2} + 4 x + 5)

= \frac{1}{3 x ^{2} + 4 x + 5} \frac{d}{d x} (3 x^{2} + 4 x + 5)

\frac{d}{d x} (3 x^{2} + 4 x + 5) = 6 x + 4

= \frac{1}{3 x ^{2} + 4 x + 5} (6 x + 4)

Simplify

\frac{1}{3 x ^{2} + 4 x + 5} (6 x + 4) : \frac{6 x + 4}{3 x ^{2} + 4 x + 5}

= \frac{6 x + 4}{3 x ^{2} + 4 x + 5}

\frac{( 1 - cos ( x ) )}{( 1 + cos ( x ) )}

\frac{d}{d t} (10 - 2 t)

y = x^{- 3}

(5^{x})^{x}

(\frac{( a + x )}{( a - x )})^{\frac{3}{2}}

What is the derivative of ln(3x^2+4x+5) ?
The derivative of ln(3x^2+4x+5) is (6x+4)/(3x^2+4x+5)
What is the first derivative of ln(3x^2+4x+5) ?
The first derivative of ln(3x^2+4x+5) is (6x+4)/(3x^2+4x+5)