What is the derivative of (2+xsqrt(x)) ?

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

What is the first derivative of (2+xsqrt(x)) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = 2 + x, g = x

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

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

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

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

Simplify

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

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

f (x) = x^{2} + 9, (- 5, 34)

\int 1 - e^{2 x} d x

1 - x^{2}, 4 - 4 x

\int (3 x + 5)^{4} d x

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