Question

2 multiple choice 1 point
what is the derivative of ( x + 3 )?
1
( x )
4
3
( x^{-1} )
clear my selection

Explanation:

Step1: Apply sum rule of derivatives

The sum rule states that if \(y = u + v\), then \(y^\prime=u^\prime + v^\prime\). Let \(u = x\) and \(v = 3\).

Step2: Differentiate \(u=x\)

Using the power rule \(\frac{d}{dx}(x^n)=nx^{n - 1}\), for \(n = 1\), \(\frac{d}{dx}(x)=1\times x^{1-1}=1\).

Step3: Differentiate \(v = 3\)

The derivative of a constant \(C\) (here \(C = 3\)) is \(0\), i.e., \(\frac{d}{dx}(3)=0\).

Step4: Find the derivative of \(y=x + 3\)

By the sum rule \(y^\prime=\frac{d}{dx}(x)+\frac{d}{dx}(3)=1+0\).

Answer:

1