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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

y^{^{'}} = 20 - 5 y

\int sin^{2} (x) x d x

y^{^{'}} = - a y + b

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

\frac{d}{d x} (x e^{(- \frac{x ^{2}}{8})})

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