What is the first derivative of x+h ?

The first derivative of x+h is 1

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derivative of x+h

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

1

Solution steps

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

Treat

h

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} + \frac{d h}{d x}

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

\frac{d h}{d x} = 0

= 1 + 0

Simplify

= 1

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

x \to 0 lim (\frac{x ^{2}}{x - 2})

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5 x^{3}