Your answer is correct, but it's not as simplified as it can be. Also, using the chain rule led to a lot of unnecessary work that could have been avoided by simplifying the expression first.Jim4592 said:Homework Statement
Find ds/dt for s=(t2)(1/7)
Homework Equations
I attempted to find the answer by using the chain rule...
The Attempt at a Solution
ds/dt = (1/7)*(t2)-(6/7)*(2t)
ds/dt = (2/7)*t*(t2)-(6/7)
Jim4592 said:I believe that would be the answer but the problem is that the answer key in the book tells me that ds/dt = (2/7)t-(5/7)
I don't understand what they did to cancel out the t2 ang get the power to be -5/7
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is calculated as the slope of a tangent line to the curve of the function at that point.
The derivative allows us to analyze the behavior of a function and understand how it changes over time or in relation to other variables. It is also used to find maximum and minimum points of a function, which is useful in optimization problems.
The derivative is calculated using a mathematical formula, which varies depending on the type of function. For example, the derivative of a polynomial function is found by applying the power rule, while the derivative of a trigonometric function is found using the chain rule.
Derivatives have many real-life applications, such as in physics to calculate velocity and acceleration, in economics to analyze the rate of change in demand and supply, and in engineering to optimize designs and predict future trends.
Some common mistakes when finding derivatives include forgetting to apply the chain rule or product rule, incorrectly applying the power rule, and not simplifying the final answer. It is important to carefully follow the rules and apply them correctly to avoid errors.