differentiate (x+1)^2 — step-by-step solution

Let's differentiate:

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

Apply the differentiation rule:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{n - 1}

with f =

x + 1

ⓘ The derivative of x^n is n*x^(n-1):

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

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

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

ⓘ The derivative of a sum is the sum of the derivatives:

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

1 + 0

2 \cdot (1 + 0) \cdot (x + 1)

ⓘ Adding 0 changes nothing:

1 + 0

1

▶Derivative:

2 \cdot (x + 1)