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

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

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

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

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derivative of

x (1 + x)^{3}

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

Solution steps

\frac{d}{d x} (x (1 + x)^{3})

Apply the Product Rule:

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

f = x, g = (1 + x)^{3}

= \frac{d x}{d x} (1 + x)^{3} + \frac{d}{d x} ((1 + x)^{3}) x

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

\frac{d}{d x} ((1 + x)^{3}) = 3 (1 + x)^{2}

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

Simplify

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

\frac{d}{d x} ((x - a) p - p^{2})

\frac{- 4}{x}

3 t^{5} + 3 t^{3} - 5

(2 x + 3)^{3}

y = 3 x (\frac{x}{2 + 2})

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