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

x \to 0 + lim (tan^{x} (5 x))

x y^{^{'}} + (1 - x) y = 1

\int e^{\frac{x ^{2}}{2}} x d x

x \to \infty lim (x \cdot e^{- \frac{x}{2}})

y = 4 - x^{2}, y = x^{2} - 4