What is the derivative of f(x)=sqrt(x+2)*sqrt(x+2) ?

The derivative of f(x)=sqrt(x+2)*sqrt(x+2) is 1

What is the first derivative of f(x)=sqrt(x+2)*sqrt(x+2) ?

The first derivative of f(x)=sqrt(x+2)*sqrt(x+2) is 1

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derivative of

f (x) = x + 2 \cdot x + 2

1

Solution steps

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

Apply the Product Rule:

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

f = x + 2, g = x + 2

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

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

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

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

Simplify

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

= 1

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What is the derivative of f(x)=sqrt(x+2)*sqrt(x+2) ?
The derivative of f(x)=sqrt(x+2)*sqrt(x+2) is 1
What is the first derivative of f(x)=sqrt(x+2)*sqrt(x+2) ?
The first derivative of f(x)=sqrt(x+2)*sqrt(x+2) is 1