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

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

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

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

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derivative of

x (x^{2} + 1)

3 x^{2} + 1

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x^{2} + 1) + 2 xx

Simplify

1 \cdot (x^{2} + 1) + 2 xx : 3 x^{2} + 1

= 3 x^{2} + 1

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

sec^{2} (7 x)

(y + 1) y^{^{'}} + x (y^{2} + 2 y) = x

\int \frac{x ^{2} + 16}{x} d x

\frac{d}{d x} (2 x^{3} - 8 x)

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