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Popular >

derivative of sqrt(ln(x+1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of (x^2+7)ln(x)

\int (x^{2} + 7) ln (x) d x

integral of sqrt((1+x)/(1-x))

\int \frac{1 + x}{1 - x} d x

integral of (x^2+2x-1)/(2x^3+3x^2-2x)

\int \frac{x ^{2} + 2 x - 1}{2 x ^{3} + 3 x ^{2} - 2 x} d x

derivative of x^2-5x+4

\frac{d}{d x} (x^{2} - 5 x + 4)

(dy)/(dx)=sqrt(y^2-9),y(5)=3

\frac{d y}{d x} = y^{2} - 9, y (5) = 3

Frequently Asked Questions (FAQ)

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