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

The derivative of in(x+sqrt(1+x^2)) is i((nsqrt(1+x^2)+nx)sqrt(1+x^2))/(1+x^2)

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

The first derivative of in(x+sqrt(1+x^2)) is i((nsqrt(1+x^2)+nx)sqrt(1+x^2))/(1+x^2)

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

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

Solution steps

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

Simplify

in (x + 1 + x^{2}) : i (n 1 + x^{2} + n x)

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (n x) = n

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

Rewrite

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

in standard complex form:

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

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

f (x) = 2 x^{3} - x^{2} + 1, (1, 2)

\frac{( 4 x - 2 ) ^{4}}{( - 5 x + 1 ) ^{5}}

f (x) = (\frac{1}{x - 3})^{2}

x^{3} + 2 x^{2} + 1

\int \frac{x ^{3}}{3} - \frac{3}{x ^{3}} d x

What is the derivative of in(x+sqrt(1+x^2)) ?
The derivative of in(x+sqrt(1+x^2)) is i((nsqrt(1+x^2)+nx)sqrt(1+x^2))/(1+x^2)
What is the first derivative of in(x+sqrt(1+x^2)) ?
The first derivative of in(x+sqrt(1+x^2)) is i((nsqrt(1+x^2)+nx)sqrt(1+x^2))/(1+x^2)