What is the derivative of In(x+sqrt(x^2+1)) ?

The derivative of In(x+sqrt(x^2+1)) is In(1+x/(sqrt(x^2+1)))

What is the first derivative of In(x+sqrt(x^2+1)) ?

The first derivative of In(x+sqrt(x^2+1)) is In(1+x/(sqrt(x^2+1)))

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\frac{d}{d x} (I n (x + x^{2} + 1))

I n (1 + \frac{x}{x ^{2} + 1})

Solution steps

\frac{d}{d x} (I n (x + x^{2} + 1))

Treat

n, I

as a constant

Take the constant out:

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

= I n \frac{d}{d x} (x + x^{2} + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= I n (\frac{d x}{d x} + \frac{d}{d x} (x^{2} + 1))

\frac{d x}{d x} = 1

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

= I n (1 + \frac{x}{x ^{2} + 1})

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