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

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

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

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

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

2 x + 1

Solution steps

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

Apply the Product Rule:

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

f = x, g = x + 1

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

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

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

= 1 \cdot (x + 1) + 1 \cdot x

Simplify

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

= 2 x + 1

\frac{d}{d x} (8^{x - 5})

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

y^{^{''}} + 25 y = 30 sin (5 t)

x \to 0 lim (x^{2})

\frac{d}{d x} (ln (x + x^{2} - 12))