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Popular >

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

Solution

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

Solution

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})

Popular Examples

derivative of sqrt(x-8)derivative of

x - 8

(dy)/(dx)+1/x y=8x^2

\frac{d y}{d x} + \frac{1}{x} y = 8 x^{2}

limit as x approaches-2-of 4/(x+2)

x \to - 2 - lim (\frac{4}{x + 2})

limit as x approaches-9 of (x^2-2)/(9-x)

x \to - 9 lim (\frac{x ^{2} - 2}{9 - x})

integral of 2/(sec(x))

\int \frac{2}{sec ( x )} d x

Frequently Asked Questions (FAQ)

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)))