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Popular >

derivative of 1/2 ln^2(x)

Solution

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

Solution

\frac{ln ( x )}{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:

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

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

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

= \frac{1}{2} \cdot 2 ln (x) \frac{1}{x}

Simplify

\frac{1}{2} \cdot 2 ln (x) \frac{1}{x} : \frac{ln ( x )}{x}

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

Popular Examples

derivative of-7csc(5x)e^{3x}derivative of

- 7 csc (5 x) e^{3 x}

integral from-2 to 2x of (3t^2+2t)

\int_{- 2}^{2 x} (3 t^{2} + 2 t) d t

integral from 0 to 4 of |x^2-9|

\int_{0}^{4} x^{2} - 9 d x

inverse oflaplace 3/(2s+1)inverse laplace

\frac{3}{2 s + 1}

tangent of f(x)=14-e^x tangent of

f (x) = 14 - e^{x}

Frequently Asked Questions (FAQ)

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