What is the derivative of aln(2x+b) ?

The derivative of aln(2x+b) is (2a)/(2x+b)

What is the first derivative of aln(2x+b) ?

The first derivative of aln(2x+b) is (2a)/(2x+b)

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\frac{d}{d x} (a ln (2 x + b))

\frac{2 a}{2 x + b}

Solution steps

\frac{d}{d x} (a ln (2 x + b))

Take the constant out:

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

= a \frac{d}{d x} (ln (2 x + b))

Apply the chain rule:

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

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

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

= a \frac{1}{2 x + b} \cdot 2

Simplify

a \frac{1}{2 x + b} \cdot 2 : \frac{2 a}{2 x + b}

= \frac{2 a}{2 x + b}

f (x) = (ln (x))^{3}

\frac{d y}{d x} - \frac{1}{x} y = e^{(\frac{y}{x})}

x \to π lim ((x - π) tan (\frac{x}{2}))

\frac{\partial}{\partial x} (x y + yz + zy)

What is the derivative of aln(2x+b) ?
The derivative of aln(2x+b) is (2a)/(2x+b)
What is the first derivative of aln(2x+b) ?
The first derivative of aln(2x+b) is (2a)/(2x+b)