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

The derivative of f(x)=(x+sqrt(2x)) is 1+1/(sqrt(2)\sqrt{x)}

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

The first derivative of f(x)=(x+sqrt(2x)) is 1+1/(sqrt(2)\sqrt{x)}

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derivative of

f (x) = (x + 2 x)

1 + \frac{1}{2 x}

Solution steps

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

Simplify

(x + 2 x) : x + 2 x

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

What is the derivative of f(x)=(x+sqrt(2x)) ?
The derivative of f(x)=(x+sqrt(2x)) is 1+1/(sqrt(2)\sqrt{x)}
What is the first derivative of f(x)=(x+sqrt(2x)) ?
The first derivative of f(x)=(x+sqrt(2x)) is 1+1/(sqrt(2)\sqrt{x)}