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Popular >

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

Solution

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

Solution

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

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

Multiply fractions:

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

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

Popular Examples

limit as t approaches 1-of (2t)/(t^2-1)

t \to 1 - lim (\frac{2 t}{t ^{2} - 1})

y^{^{''}} - 2 y + 4 y = 0

integral of 11x^{10}-(10)/(x^{10)}

\int 11 x^{10} - \frac{10}{x ^{10}} d x

integral of 1/(sqrt(9-4x^2))

\int \frac{1}{9 - 4 x ^{2}} d x

derivative of cos(2x)*ln(3x-5)derivative of

cos (2 x) \cdot ln (3 x - 5)

Frequently Asked Questions (FAQ)

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