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