Practice with power rule for derivatives and limits

The Power Rule states that if $$f(x) = x^n$$ , then the derivative $$f'(x) = n*x^{n-1}$$ .

$$f'(x) = 15x^2 - 2$$ .

A limit is a value that a function approaches as the input approaches some value.

$$2$$ .

The equation of a tangent line at point (a, f(a)) is given by: $$y - f(a) = f'(a)(x - a)$$ .

$$f'(x) = 2x + 3; f'(1) = 5$$ .

DNE stands for 'Does Not Exist', indicating that the limit does not approach a finite value.

$$f'(x) = 4x + 3$$ .

$$f'(x) = -\frac{1}{x^2}$$ .

Evaluate the function's behavior as x increases without bound, often simplifying the function.