What is the derivative of x+sqrt(x)+3 ?

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

What is the first derivative of x+sqrt(x)+3 ?

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

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

\frac{1}{2 x} + 1

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (3) = 0

= 1 + \frac{1}{2 x} + 0

Simplify

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

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\int \frac{1}{( 36 + x ^{2} ) ^{2}} d x

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