Question

rules of differentation​

Answer 1

Answer:

hey mate

Determining the derivative of a function from first principles requires a long calculation and it is easy to make mistakes. However, we can use this method of finding the derivative from first principles to obtain rules which make finding the derivative of a function much simpler

Differentiate the following from first principles:

f(x)=x

f(x)=−4x

f(x)=x2

f(x)=3x2

f(x)=−x3

f(x)=2x3

f(x)=1x

f(x)=−2x

Complete the table:

f(x). f′(x)

x

−4x

x2

3x2

−x3

2x3

1x

−2x

Can you identify a pattern for determining the derivative

The derivative of a constant is equal to zero. ...

The derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of the function. ...

The derivative of a sum is equal to the sum of the derivatives.