#### To determine

**To find:** The derivative of the function F(y)=5r3.

#### Answer

The derivative of the function F(y)=5r3 is −15r4.

#### Explanation

**Given:**

The function, F(y)=5r3.

**Formula used:**

**The Constant Multiple Rule:**

If *c* is a constant and F(r) is a differentiable function, then the constant multiple rule is,

ddr[c⋅F(r)]=c⋅ddrF(r) (1)

**The Power Rule:**

If n is any real number, then the power rule is,

ddr(rn)=nrn−1 (2)

**Calculation:**

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.

F′(r)=ddr(F(r)) =ddr(5r−3)

Apply the constant multiplicative rule as shown in equation (1).

F′(r)=5ddr(r−3)

Apply the power rule as shown in equation (2).

F′(r)=5(−3)r−3−1=−15r−4=−15r4

Therefore, the derivative of the function F(y)=5r3 is −15r4_.