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

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

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

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

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

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

Simplify

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

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

\int_{0}^{4} f (x) d x

(x - 2) y^{^{'}} + y = 3 x^{2} + 2 x

n = 0 \sum \infty \frac{1}{( 2 n + 1 ) ^{4}}

x + 3 y = 34, x + 6 = y^{2}

\frac{d}{d x} (9 x^{2} e^{- x})

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