1-22 Differentiate the function.
To find: The derivative of the function F(y)=5r3.
The derivative of the function F(y)=5r3 is −15r4.
The function, F(y)=5r3.
The Constant Multiple Rule:
If c is a constant and F(r) is a differentiable function, then the constant multiple rule is,
The Power Rule:
If n is any real number, then the power rule is,
The function F(r)=5r3 can be written as F(r)=5r−3.
The derivative of F(r)=5r−3 is F′(r) as follows.
Apply the constant multiplicative rule as shown in equation (1).
Apply the power rule as shown in equation (2).
Therefore, the derivative of the function F(y)=5r3 is −15r4_.