. 𝑓(𝑥) = 3𝑥4 − 4𝑥3

To find the derivative of the function 𝑓(𝑥) = 3𝑥^4 - 4𝑥^3, we can use the power rule for differentiation.

Step 1: Identify the power of 𝑥 in each term of the function. In this case, we have 𝑥^4 and 𝑥^3.

Step 2: Apply the power rule, which states that the derivative of 𝑥^n is equal to n𝑥^(n-1).

For the term 3𝑥^4, the derivative is: d/d𝑥 (3𝑥^4) = 4 * 3𝑥^(4-1) = 12𝑥^3.

For the term -4𝑥^3, the derivative is: d/d𝑥 (-4𝑥^3) = 3 * -4𝑥^(3-1) = -12𝑥^2.

Step 3: Combine the derivatives of each term to find the derivative of the entire function.

The derivative of 𝑓(𝑥) = 3𝑥^4 - 4𝑥^3 is: 𝑓'(𝑥) = 12𝑥^3 - 12𝑥^2.