What is the derivative of y=(x+1)(sqrt(x)+2) ?

The derivative of y=(x+1)(sqrt(x)+2) is (3x+1)/(2sqrt(x))+2

What is the first derivative of y=(x+1)(sqrt(x)+2) ?

The first derivative of y=(x+1)(sqrt(x)+2) is (3x+1)/(2sqrt(x))+2

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derivative of

y = (x + 1) (x + 2)

\frac{3 x + 1}{2 x} + 2

Solution steps

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

Apply the Product Rule:

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

f = x + 1, g = x + 2

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

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

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

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

Simplify

1 \cdot (x + 2) + \frac{1}{2 x} (x + 1) : \frac{3 x + 1}{2 x} + 2

= \frac{3 x + 1}{2 x} + 2

What is the derivative of y=(x+1)(sqrt(x)+2) ?
The derivative of y=(x+1)(sqrt(x)+2) is (3x+1)/(2sqrt(x))+2
What is the first derivative of y=(x+1)(sqrt(x)+2) ?
The first derivative of y=(x+1)(sqrt(x)+2) is (3x+1)/(2sqrt(x))+2