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

The derivative of x(x+1^2) is 3x^2+4x+1

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

The first derivative of x(x+1^2) is 3x^2+4x+1

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

3 x^{2} + 4 x + 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x + 1)^{2} + 2 (x + 1) x : 3 x^{2} + 4 x + 1

= 3 x^{2} + 4 x + 1

(3 x - 1)^{2} (x^{2} + 1)^{2}

y^{^{'}} - y = 9 t

\int sec^{6} (3 y) tan^{2} (3 y) d y

\frac{\partial}{\partial x} ((2 x) (3 z))

\frac{d y}{d x} = 6 y

What is the derivative of x(x+1^2) ?
The derivative of x(x+1^2) is 3x^2+4x+1
What is the first derivative of x(x+1^2) ?
The first derivative of x(x+1^2) is 3x^2+4x+1