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

The derivative of x^2sqrt(x+1) is (5x^2+4x)/(2sqrt(x+1))

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

The first derivative of x^2sqrt(x+1) is (5x^2+4x)/(2sqrt(x+1))

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derivative of

x^{2} x + 1

\frac{5 x ^{2} + 4 x}{2 x + 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = x + 1

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

2 x x + 1 + \frac{1}{2 x + 1} x^{2} : \frac{5 x ^{2} + 4 x}{2 x + 1}

= \frac{5 x ^{2} + 4 x}{2 x + 1}

\frac{d}{d x} ((x^{5} + 5)^{\frac{4}{3}} tan (2 x))

x \to \infty lim (4 x - x^{2})

\int 2 x e^{9 x} d x

\frac{\partial}{\partial y} (x^{\frac{3}{2}} - 3 y)

\frac{6}{s ^{2} - 5 s - 20}

What is the derivative of x^2sqrt(x+1) ?
The derivative of x^2sqrt(x+1) is (5x^2+4x)/(2sqrt(x+1))
What is the first derivative of x^2sqrt(x+1) ?
The first derivative of x^2sqrt(x+1) is (5x^2+4x)/(2sqrt(x+1))