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

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

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

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

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derivative of

x (1 + x)^{2}

3 x^{2} + 4 x + 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{( 3 x ^{4} + 9 x ^{2} + 1 )}{x}

e^{x^{2} - y^{2}}

(8 x^{2} + 3 x + 1) \cdot 0.2 x

(sec (x^{2}))^{3}

- 2 + 3 sin (x)

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