Answer :
The derivative of f(x) = x⁵⁰, is (c). f'(x) = 50x⁴⁹.
To determine the derivative, we apply the power rule of differentiation. The power rule of differentiation says that if f(x) = xⁿ, then f'(x) = nxⁿ⁻¹.
Given f(x) = x⁵⁰:
- Identify the exponent: n = 50.
- use the power rule of differentiation : f'(x) = 50x⁵⁰⁻¹ = 50x⁴⁹.
Therefore, the correct answer is C. f'(x) = 50x⁴⁹.
Answer:
f'(x) = 50x⁴⁹
Step-by-step explanation:
f(x) = y = x⁵⁰.
Let u = x and y = u⁵⁰
du/dx = 1 and dy/du = 50u⁴⁹
Using Chain rule,
dy/dx = dy/du × du/dx
dy/dx = 50u⁴⁹ × 1
dy/dx = 50u⁴⁹ Substitute the value of u
Therefore,
dy/dx = f'(x) = 50x⁴⁹
