What is the derivative of f(x)=xsqrt(x+3) ?

The derivative of f(x)=xsqrt(x+3) is (3x+6)/(2sqrt(x+3))

What is the first derivative of f(x)=xsqrt(x+3) ?

The first derivative of f(x)=xsqrt(x+3) is (3x+6)/(2sqrt(x+3))

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derivative of

f (x) = x x + 3

\frac{3 x + 6}{2 x + 3}

Solution steps

\frac{d}{d x} (x x + 3)

Apply the Product Rule:

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

f = x, g = x + 3

= \frac{d x}{d x} x + 3 + \frac{d}{d x} (x + 3) x

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot x + 3 + \frac{1}{2 x + 3} x : \frac{3 x + 6}{2 x + 3}

= \frac{3 x + 6}{2 x + 3}

What is the derivative of f(x)=xsqrt(x+3) ?
The derivative of f(x)=xsqrt(x+3) is (3x+6)/(2sqrt(x+3))
What is the first derivative of f(x)=xsqrt(x+3) ?
The first derivative of f(x)=xsqrt(x+3) is (3x+6)/(2sqrt(x+3))