- #1
Joyci116
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Homework Statement
f(x)=(x^{2}-x)(sin(x))
Homework Equations
Chain rule
Product rule
The Attempt at a Solution
f'g(x)*g'(x)
cosx
(2x-x)(cosx)
Would you use the product rule after using the power rule and chain rule?
?Joyci116 said:Homework Statement
f(x)=(x^{2}-x)(sin(x))
Homework Equations
Chain rule
Product rule
The Attempt at a Solution
f'g(x)*g'(x)
cosx
No. Use the product rule first. You don't need the chain rule at all.Joyci116 said:(2x-x)(cosx)
Would you use the product rule after using the power rule and chain rule?
The derivative is a mathematical concept that represents the rate of change of a function at a specific point. It measures how much the output of a function changes with respect to its input at that point.
Finding the derivative is important because it allows us to understand the behavior of a function at a given point and make predictions about its future values. It also helps us to optimize functions and solve real-world problems in fields such as physics, economics, and engineering.
The derivative of a function can be calculated using the limit definition of derivative, which is the change in the output divided by the change in the input as the change in input approaches zero. Alternatively, we can use differentiation rules, such as the power rule and chain rule, to find the derivative of more complex functions.
Yes, the derivative of a function can be negative. This means that the function is decreasing at that point, and the slope of the tangent line to the graph of the function is negative. A negative derivative can also represent a decreasing rate of change.
Finding the derivative has numerous applications in various fields such as physics, economics, and engineering. Some examples include optimizing production and cost functions in economics, calculating velocity and acceleration in physics, and determining the maximum and minimum values of a function in engineering.