What is the derivative of e^{(x+sqrt(x^2+1)}) ?

The derivative of e^{(x+sqrt(x^2+1)}) is e^{x+sqrt(x^2+1)}(1+x/(sqrt(x^2+1)))

What is the first derivative of e^{(x+sqrt(x^2+1)}) ?

The first derivative of e^{(x+sqrt(x^2+1)}) is e^{x+sqrt(x^2+1)}(1+x/(sqrt(x^2+1)))

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

e^{x + x^{2} + 1} (1 + \frac{x}{x ^{2} + 1})

Solution steps

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

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (8 x ln (x))

r^{2} - 5 x^{2}

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

\int (3 e^{x} + 8 x^{3} + 4 x) d x

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