Introduction to Power Rule for Derivatives

Front

What is the Power Rule for Derivatives?

Back

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

Front

Find the derivative of f(x) = 5x^3.

Back

f'(x) = 15x^2.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Find the derivative of f(x) = 7x^2 + 3x + 1.

Back

f'(x) = 14x + 3.

Front

What is the derivative of f(x) = x^4?

Back

f'(x) = 4x^3.

Front

Find the derivative of f(x) = 12 - 8x.

Back

f'(x) = -8.

Front

What is the derivative of f(x) = x^n when n is a negative integer?

Back

f'(x) = n*x^(n-1), where n is negative.

Front

Find dy/dx for y = 4x^3 + 3x + 1.

Back

dy/dx = 12x^2 + 3.

Front

What is the equation of the tangent line at a point (a, f(a))?

Back

y - f(a) = f'(a)(x - a).

Front

Find the derivative of f(x) = x^3 + x^2 + 3.

Back

f'(x) = 3x^2 + 2x.