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

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

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

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

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

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

Solution steps

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

Treat

a, n, I

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

y^{^{'}} + 4 y = e^{- 4 t}

\frac{d}{d x} (\frac{7 x}{x ^{2} + 1})

\int \frac{1}{x ^{2} + 5} d x

sin (y) d x + cos (x) d y = 0

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