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Popular >

derivative of 1/2 ln(2x)

Solution

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

Solution

\frac{1}{2 x}

Solution steps

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

Take the constant out:

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

= \frac{1}{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

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

Simplify

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

= \frac{1}{2 x}

Popular Examples

(dy)/(dt)=(15-(3y)/(360-2t))

\frac{d y}{d t} = (15 - \frac{3 y}{360 - 2 t})

(\partial)/(\partial v)(ucos(v))

\frac{\partial}{\partial v} (u cos (v))

derivative of f(x)=2x^2-6x derivative of

f (x) = 2 x^{2} - 6 x

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\int_{- π}^{2 π} cos^{2} (x) d x

limit as x approaches 0 of e^{1/x ln(1+x^2)}

x \to 0 lim (e^{\frac{1}{x} l n (1 + x^{2})})

Frequently Asked Questions (FAQ)

What is the derivative of 1/2 ln(2x) ?
The derivative of 1/2 ln(2x) is 1/(2x)
What is the first derivative of 1/2 ln(2x) ?
The first derivative of 1/2 ln(2x) is 1/(2x)