What is the derivative of x^2*sqrt(1+x^2) ?

The derivative of x^2*sqrt(1+x^2) is (3x^3+2x)/(sqrt(1+x^2))

What is the first derivative of x^2*sqrt(1+x^2) ?

The first derivative of x^2*sqrt(1+x^2) is (3x^3+2x)/(sqrt(1+x^2))

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derivative of

x^{2} \cdot 1 + x^{2}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x 1 + x^{2} + \frac{x}{1 + x ^{2}} x^{2} : \frac{3 x ^{3} + 2 x}{1 + x ^{2}}

= \frac{3 x ^{3} + 2 x}{1 + x ^{2}}

What is the derivative of x^2*sqrt(1+x^2) ?
The derivative of x^2*sqrt(1+x^2) is (3x^3+2x)/(sqrt(1+x^2))
What is the first derivative of x^2*sqrt(1+x^2) ?
The first derivative of x^2*sqrt(1+x^2) is (3x^3+2x)/(sqrt(1+x^2))