appplejack said:Homework Statement
f(x) = x(x-5)^4
Homework Equations
The Attempt at a Solution
I used product rule and chain rule so,
1(x-5)^4 + 4x(x-5)^3(1)
The answer to this question is 5(x-5)^3(x-1). I left it like the answer above. I don't know how to expand (x-5)^4. Thanks.
appplejack said:Homework Statement
f(x) = x(x-5)^4
Homework Equations
The Attempt at a Solution
I used product rule and chain rule so,
1(x-5)^4 + 4x(x-5)^3(1)
The answer to this question is 5(x-5)^3(x-1). I left it like the answer above. I don't know how to expand (x-5)^4. Thanks.
The derivative of a function is a measure of how much the output of the function changes with respect to the input. It is the slope of the tangent line at a specific point on the function's graph.
Taking the derivative allows us to analyze how a system or process is changing over time. It is used in many scientific fields such as physics, engineering, and economics to model and predict the behavior of systems.
To take the derivative of a function, you need to use the rules of differentiation. These include the power rule, product rule, quotient rule, and chain rule. It involves finding the limit of a difference quotient as the change in input approaches zero.
Some common mistakes when taking the derivative include forgetting to apply the correct differentiation rule, making algebraic errors, and not simplifying the final result. It is also important to pay attention to the domain and range of the function to avoid taking derivatives of discontinuous or undefined points.
The best way to practice and improve your skills in taking derivatives is to solve a variety of problems using different differentiation rules. You can also use online resources or textbooks to find practice problems and solutions. It is also helpful to understand the applications of derivatives in real-life situations.