calculus power rule

Front

What is the Power Rule in calculus?

Back

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

Front

Differentiate \( y = x^5 \) using the Power Rule.

Back

\( y' = 5x^{4} \) (Applying the Power Rule).

Front

Differentiate \( y = 7x^3 \) using the Power Rule.

Back

\( y' = 21x^{2} \) (Applying the Power Rule).

Front

Differentiate \( y = 12x^{-2} \) using the Power Rule.

Back

\( y' = -24x^{-3} \) (Applying the Power Rule).

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Differentiate \( y = 2\pi \).

Back

\( y' = 0 \) (The derivative of a constant is 0).

Front

Differentiate \( y = 5x^4 \).

Back

\( y' = 20x^{3} \) (Applying the Power Rule).

Front

Differentiate \( m(x) = 3x^2 + 2x + 1 \).

Back

\( m'(x) = 6x + 2 \) (Using the Power Rule for each term).

Front

What is the derivative of \( f(x) = x^3 \)?

Back

\( f'(x) = 3x^{2} \) (Applying the Power Rule).

Front

If \( f(x) = x^n \), what is the derivative when \( n = 0 \)?

Back

The derivative is 0, since \( f(x) = 1 \) (a constant).