Question

Find the derivative of the function f(x) = x - 7x³.

Answer 1

The derivative of the function f(x) = x - 7x³ is found using the power rule, resulting in f'(x) = 1 - 21x².

Step-by-step explanation:

To find the derivative of the function f(x) = x - 7x³, we use the power rule of differentiation. The power rule states that if f(x) = xⁿ, then f'(x) = nxⁿ⁻¹. Applying this to our function, we get:

f'(x) = d/dx (x) - d/dx (7x³)

f'(x) = 1 - 21x²

So the derivative of f(x) = x - 7x³ is f'(x) = 1 - 21x².