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Popular >

derivative of ln(x)sqrt(x)

Solution

derivative of

ln (x) x

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = x

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

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

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

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

Simplify

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

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

Popular Examples

tangent of f(x)=x^4+4e^x,(0,4)tangent of

f (x) = x^{4} + 4 e^{x}, (0, 4)

(dy)/(dt)=-2(y-4)

\frac{d y}{d t} = - 2 (y - 4)

integral of (sqrt(x^2+16))/(x^4)

\int \frac{x ^{2} + 16}{x ^{4}} d x

limit as x approaches 1 of x^2+3x-4

x \to 1 lim (x^{2} + 3 x - 4)

derivative of ((x^2e^x))/(x^2+e^x)derivative of

\frac{( x ^{2} e ^{x} )}{x ^{2} + e ^{x}}

Frequently Asked Questions (FAQ)

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