What is the derivative of h(x)=ln(x+sqrt(x^2-11)) ?

The derivative of h(x)=ln(x+sqrt(x^2-11)) is 1/(sqrt(x^2-11))

What is the first derivative of h(x)=ln(x+sqrt(x^2-11)) ?

The first derivative of h(x)=ln(x+sqrt(x^2-11)) is 1/(sqrt(x^2-11))

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derivative of

h (x) = ln (x + x^{2} - 11)

\frac{1}{x ^{2} - 11}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 11))

Apply the chain rule:

\frac{1}{x + x ^{2} - 11} \frac{d}{d x} (x + x^{2} - 11)

= \frac{1}{x + x ^{2} - 11} \frac{d}{d x} (x + x^{2} - 11)

\frac{d}{d x} (x + x^{2} - 11) = 1 + \frac{x}{x ^{2} - 11}

= \frac{1}{x + x ^{2} - 11} (1 + \frac{x}{x ^{2} - 11})

Simplify

\frac{1}{x + x ^{2} - 11} (1 + \frac{x}{x ^{2} - 11}) : \frac{1}{x ^{2} - 11}

= \frac{1}{x ^{2} - 11}

x, \frac{1}{2} x

x^{2} y^{^{''}} - 2 x y^{^{'}} + 2 y = x^{4} e^{x}

\int \frac{1}{2} y^{2} d y

\frac{s + 2}{s ^{2} + 4 s + 5}

y^{^{''}} + 25 y = t sin (4 t)

What is the derivative of h(x)=ln(x+sqrt(x^2-11)) ?
The derivative of h(x)=ln(x+sqrt(x^2-11)) is 1/(sqrt(x^2-11))
What is the first derivative of h(x)=ln(x+sqrt(x^2-11)) ?
The first derivative of h(x)=ln(x+sqrt(x^2-11)) is 1/(sqrt(x^2-11))