Step 1: Identify the function you want to differentiate, which is f(x) = x^5 + 3x^3 - 2x.
Step 2: Apply the power rule for differentiation. The power rule states that if you have x^n, the derivative is n*x^(n-1).
Step 3: Differentiate each term in the function separately.
Step 4: For the first term x^5, apply the power rule: the derivative is 5*x^(5-1) = 5x^4.
Step 5: For the second term 3x^3, apply the power rule: the derivative is 3*3*x^(3-1) = 9x^2.
Step 6: For the third term -2x, apply the power rule: the derivative is -2*1*x^(1-1) = -2.
Step 7: Combine all the derivatives from the previous steps: f'(x) = 5x^4 + 9x^2 - 2.
Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Power Rule – A rule used in differentiation that states if f(x) = x^n, then f'(x) = n*x^(n-1).
