#### To determine

**To find:** The value of F′(5).

#### Answer

The value of F′(5) is F′(5)=24.

#### Explanation

**Given:**

The function is F(x)=f(g(x)).

The values are f(−2)=8,f′(−2)=4,f′(5)=3,g(5)=−2 and g′(5)=6.

**Result used: Chain Rule**

If *h* is differentiable at *x* and *g* is differentiable at h(x), then the composite function F=g∘h defined by F(x)=g(h(x)) is differentiable at *x* and F′ is given by the product

F′(x)=g′(h(x))⋅h′(x) (1)

**Calculation:**

Obtain the derivative of F(x)=f(g(x)).

F′(x)=ddx(F(x))=ddx(f(g(x)))

Apply the chain rule as shown in equation (1)

F′(x)=f′(g(x))⋅g′(x) (2)

Substitute x=5 in equation (2),

F′(5)=f′(g(5))⋅g′(5)

Substitute g(5)=−2 in the above equation,

F′(5)=f′(−2)⋅g′(5)

Substitute f′(−2)=4 and g′(5)=6 in the above equation,

F′(5)=4⋅6=24

Therefore, the derivative of F(5)=f(g(5)) is F′(5)=24.