#### To determine

**To find:** The derivative of the function H(u)=(3u−1)(u+2).

#### Answer

The derivative of the function H(u)=(3u−1)(u+2) is 6u+5_.

#### Explanation

**Given:**

The function, H(u)=(3u−1)(u+2).

**Formula used:**

**Derivative of a Constant Function:**

If *c* is a constant function, then ddu(c)=0 (1)

**The Constant Multiple Rule:**

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

ddu[c⋅f(u)]=c⋅dduf(u) (2)

**The Power Rule:**

If *n* is any real number, then the multiple rule is,

ddu(un)=nun−1 (3)

**The Sum Rule:**

If f(u) and g(u) are both differentiable function, then the sum rule is,

ddu[f(u)+g(u)]=ddu(f(u))+ddu(g(u)) (4)

**The Difference Rule:**

If f(u) and g(u) are both differentiable, then the difference rule is,

ddu[f(u)−g(u)]=ddu(f(u))−ddu(g(u)) (5)

**Calculation:**

The derivative of H(u)=(3u−1)(u+2) is H′(u) as follows.

H′(u)=ddu[H(u)]=ddu[(3u−1)(u+2)]=ddu(3u2+6u−u−2)=ddu(3u2+5u−2)

Apply the difference rule as shown in equation (5).

H′(u)=ddu(3u2+5u)−ddu(2)

Apply the sum rule as shown in equation (4).

H′(u)=ddu(3u2)+ddu(5u)−ddu(2)

Apply the constant multiplication rule as shown in equation (2).

H′(u)=3ddu(u2)+5ddu(u)−ddu(2)

Apply the power rule as shown in equation (3).

H′(u)=3(2u2−1)+5(1u1−1)−ddu(2)

In equation (1), apply 2 for *c*.

H′(u)=3(2u1)+5(1u0)+0=6u+5(1)=6u+5

Therefore, the derivative of the function H(u)=(3u−1)(u+2) is 6u+5_.