What is the derivative of 2ln(2x) ?

The derivative of 2ln(2x) is 2/x

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

The first derivative of 2ln(2x) is 2/x

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

\frac{2}{x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 2 \cdot \frac{1}{2 x} \cdot 2

Simplify

2 \cdot \frac{1}{2 x} \cdot 2 : \frac{2}{x}

= \frac{2}{x}

\frac{\partial}{\partial r} (r^{2 + s^{2}})

\frac{t}{t ^{2} + 1}

y^{^{''}} + 15 y^{^{'}} + 56 y = 0

\frac{d y}{d x} + 9 y = 5

t^{2} y^{^{'}} + y^{2} = t y

What is the derivative of 2ln(2x) ?
The derivative of 2ln(2x) is 2/x
What is the first derivative of 2ln(2x) ?
The first derivative of 2ln(2x) is 2/x