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Popular Calculus >

derivative of f(x)=e^xsqrt(1+x^2)

Solution

derivative of

f (x) = e^{x} 1 + x^{2}

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = 1 + x^{2}

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Multiply fractions:

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

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

Graph

Popular Examples

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\frac{d}{d x} (ln (x^{2} + 2 - y))

(\partial)/(\partial x)(x/(sin(2x)+3y+z^2))

\frac{\partial}{\partial x} (\frac{x}{sin ( 2 x ) + 3 y + z ^{2}})

integral of sinh^3(x)

\int sinh^{3} (x) d x

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x \to 0 lim (∣ x + 2 ∣)

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\int sin^{4} (\frac{x}{3}) cos (\frac{x}{3}) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^xsqrt(1+x^2) ?
The derivative of f(x)=e^xsqrt(1+x^2) is e^xsqrt(1+x^2)+(e^xx)/(sqrt(1+x^2))
What is the first derivative of f(x)=e^xsqrt(1+x^2) ?
The first derivative of f(x)=e^xsqrt(1+x^2) is e^xsqrt(1+x^2)+(e^xx)/(sqrt(1+x^2))