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

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

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

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

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derivative of

y = x x + 1

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

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

Simplify

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

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

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