#### To determine

**To Find:**

f'x if it is known that

ddxf2x=x2

#### Answer

**f'x=x28**

#### Explanation

**1. Concept:**

Solve by using differentiation rules

**2. Formula:**

(i) Chain rule:

dydx= dydududx

**3. Given:**

ddxf2x= x2

**4. Calculation:**

Find derivative of f2x

Let, u = 2x

Taking derivative of u with respect to x,

dudx=2

Then given equation becomes fu,

Now, differentiating implicitly fu with respect to x

By using Chain Rule

ddxf2x=f'ududx

Substitutethe value of

u and dudx

ddxf2x=f'2x(2)

∴2·f'2x=x2

∴f'2x=x22

Let, v=2x

∴x=v2

Substituting value of v,x

f'v=v/222

f'v=v28

Replace v by x,

f'x=x28

**Conclusion:**

Therefore,

f'x=x28