What is (\partial)/(\partial x)(xsqrt(x+1)) ?

The answer to (\partial)/(\partial x)(xsqrt(x+1)) is (3x+2)/(2sqrt(x+1))

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(\partial)/(\partial x)(xsqrt(x+1))

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = x + 1

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial 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}

\frac{d y}{d x} = 2 y

\int_{0}^{6} 3 x - x^{2} d x

\frac{1}{x - 3}

x \to 0 - lim (cos (x))

\int x cos^{4} (x) d x

What is (\partial)/(\partial x)(xsqrt(x+1)) ?
The answer to (\partial)/(\partial x)(xsqrt(x+1)) is (3x+2)/(2sqrt(x+1))