#### To determine

**To find:** The differentiation of
g(t)=4sect+tant.

#### Answer

The differentiation of
g(t)=4sect+tant is
(4tant+sect)sect_.

#### Explanation

**Formula used:**

**The Difference Rule:**

If
g(θ).and
h(θ) are both differentiable functions, then the difference rule is,

ddθ[g(θ)−h(θ)]=ddθ[g(θ)]−ddθ[h(θ)] (1)

Constant multiple rule:

ddt[c⋅f(t)]=c⋅ddtf(t) (2)

**Calculation:**

Apply the difference rule as shown in equation (1).

ddt[4sect+tant]=ddt[4sect]−ddt[tant] (3)

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

ddt[4sect+tant]=4ddt[sect]−ddt[tant] (4)

Notice that the derivative of
ddt[sect]=secttant and
ddt[tant]=sec2t.

Substitute the above derivatives in equation (4).

ddt[4sect+tant]=4(tantsect)−(sec2t)=sect(2tant+sect)

Therefore, the differentiation of
g(t)=4sect+tant is
(4tant+sect)sect_.