What is the derivative of y=xβ+e ?

The derivative of y=xβ+e is β

What is the first derivative of y=xβ+e ?

The first derivative of y=xβ+e is β

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derivative of

y = x β + e

β

Solution steps

\frac{d}{d x} (x β + e)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x β) + \frac{d e}{d x}

\frac{d}{d x} (x β) = β

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

= β + 0

Simplify

= β

\frac{d}{d x} ((\frac{x + 5}{x ^{2} + 2})^{2})

x \to 1 + lim (x - 1)

x \to 0 + lim (e^{\frac{1}{x} l n (x)})

\int_{0}^{1} \frac{7 y}{e ^{2 y}} d y

- 2 y^{^{'}} + \frac{2 y}{x} = x^{4} y^{3}