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Popular >

derivative of x^2sqrt(1+x^2)

Solution

derivative of

x^{2} 1 + x^{2}

Solution

\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}}

Popular Examples

integral of (-x^2-3x+3)^2

\int (- x^{2} - 3 x + 3)^{2} d x

derivative of-1/6 x^3-1/2 x^2+x+1+ke^k

\frac{d}{d x} (- \frac{1}{6} x^{3} - \frac{1}{2} x^{2} + x + 1 + k e^{k})

integral of 8sec^4(θ)tan^2(θ)

\int 8 sec^{4} (θ) tan^{2} (θ) d θ

integral of sqrt(3-2x)

\int 3 - 2 x d x

(\partial)/(\partial x)(xy+1/x+8/y)

\frac{\partial}{\partial x} (x y + \frac{1}{x} + \frac{8}{y})

Frequently Asked Questions (FAQ)

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