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