What is the derivative of x+{z}(x) ?

The derivative of x+{z}(x) is 1+derivative of {z}(x)

What is the first derivative of x+{z}(x) ?

The first derivative of x+{z}(x) is 1+derivative of {z}(x)

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

1 + \frac{d}{d x} (z (x))

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

What is the derivative of x+{z}(x) ?
The derivative of x+{z}(x) is 1+derivative of {z}(x)
What is the first derivative of x+{z}(x) ?
The first derivative of x+{z}(x) is 1+derivative of {z}(x)