Learn how to find the derivative of x^5. The derivative is d/dx[x^5].
Below is the graph of f(x) = x^5 and its derivative f'(x). Notice how the original function and derivative relate to each other.
Original Function:
Derivative:
This derivative represents the rate of change of the original function. The calculation follows standard differentiation rules as shown in the step-by-step solution below.
To find the derivative of x^5, we identify that the function is a power of x. This makes the Power Rule the appropriate tool for differentiation.
💡 Why this works: The Power Rule applies when a function is in the form of x raised to a constant exponent. Since x^5 fits this form, we will differentiate it using the Power Rule.
Using the Power Rule, we differentiate x^5 by bringing down the exponent as a coefficient and reducing the exponent by one.
💡 Why this works: The Power Rule states that the derivative of x^n is n*x^(n-1). For x^5, the derivative is 5*x^(5-1) = 5x^4.
Once we apply the Power Rule, we obtain the derivative 5x^4, which is the simplest form of the result.
💡 Why this works: After applying the Power Rule, the expression 5x^4 is the correct and final derivative. This result confirms that the derivative of x^5 is 5x^4.
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❌ Common Mistake:
Not simplifying the final answer
✅ Correct Approach:
Always simplify your derivative to its most reduced form
Double-check your work by comparing your steps with our solution. Use our calculator to verify each step of the differentiation process.
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