What is the derivative of (5x(5x+1)) ?

The derivative of (5x(5x+1)) is 5(10x+1)

What is the first derivative of (5x(5x+1)) ?

The first derivative of (5x(5x+1)) is 5(10x+1)

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\frac{d}{d x} ((5 x) (5 x + 1))

5 (10 x + 1)

Solution steps

\frac{d}{d x} ((5 x) (5 x + 1))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x (5 x + 1))

Apply the Product Rule:

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

f = x, g = 5 x + 1

= 5 (\frac{d x}{d x} (5 x + 1) + \frac{d}{d x} (5 x + 1) x)

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

\frac{d}{d x} (5 x + 1) = 5

= 5 (1 \cdot (5 x + 1) + 5 x)

Simplify

= 5 (10 x + 1)

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What is the derivative of (5x(5x+1)) ?
The derivative of (5x(5x+1)) is 5(10x+1)
What is the first derivative of (5x(5x+1)) ?
The first derivative of (5x(5x+1)) is 5(10x+1)