What is the derivative of In(x+1) ?

The derivative of In(x+1) is nI

What is the first derivative of In(x+1) ?

The first derivative of In(x+1) is nI

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\frac{d}{d x} (I n (x + 1))

n I

Solution steps

\frac{d}{d x} (I n (x + 1))

Treat

n, I

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= I n \frac{d}{d x} (x + 1)

Apply the Sum/Difference Rule:

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

= I n (\frac{d x}{d x} + \frac{d}{d x} (1))

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

\frac{d}{d x} (1) = 0

= I n (1 + 0)

Simplify

= n I

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