What is the derivative of 5ln(2x+6) ?

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

What is the first derivative of 5ln(2x+6) ?

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

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\frac{d}{d x} (5 ln (2 x + 6))

\frac{5}{x + 3}

Solution steps

\frac{d}{d x} (5 ln (2 x + 6))

Take the constant out:

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

= 5 \frac{d}{d x} (ln (2 x + 6))

Apply the chain rule:

\frac{1}{2 x + 6} \frac{d}{d x} (2 x + 6)

= \frac{1}{2 x + 6} \frac{d}{d x} (2 x + 6)

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

= 5 \cdot \frac{1}{2 x + 6} \cdot 2

Simplify

5 \cdot \frac{1}{2 x + 6} \cdot 2 : \frac{5}{x + 3}

= \frac{5}{x + 3}

f (x) = \frac{2 x + 6 x ^{2}}{( 1 + 6 x ) ^{2}}

\int \frac{x + 9}{x ^{2} + 8 x + 20} d x

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

\frac{d}{d t} (6 cos (2 t))

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