Question

Find the derivatives of the following using the different rules.1. f(x) = 722. f(x) = -67x

Answer 1

• (a)f'(x)=0

,

• (b)f'(x)=-67

Explanation:

(a)Given the function:

`f(x)=72`

By the rules of differentiation given below:

`\begin{gathered} (d)/(dx)(c)=0 \\ where\text{ c is a constant.} \end{gathered}`

Therefore:

`\begin{gathered} (d)/(dx)(72)=0 \\ f^(\prime)(x)=0 \end{gathered}`

(b) Given the function:

`f\mleft(x\mright)=-67x`

Using the rule of derivatives below:

`(d)/(dx)[cf(x)]=c(d)/(dx)[f(x)],c\text{ a constant}`

Applying this rule:

`\begin{gathered} (d)/(dx)[-67x]=-67(d)/(dx)[x] \\ =-67(1) \\ \implies f^(\prime)(x)=-67 \end{gathered}`

The derivative is -67.