# Finding the derivative

• Joyci116
In summary, to find the derivative of f(x)=(x2-x)(sin(x)), we can use the product rule by taking the derivative of the first term and multiplying it by the second term, then adding the derivative of the second term multiplied by the first term. This gives us (x2-x)cosx+sinx(2x-1). We do not need to use the chain rule in this case.
Joyci116

## Homework Statement

f(x)=(x2-x)(sin(x))

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?

Review the product rule !

Joyci116 said:

## Homework Statement

f(x)=(x2-x)(sin(x))

Chain rule
Product rule

## The Attempt at a Solution

f'g(x)*g'(x)
cosx
?
This looks like you're attempting to use the chain rule.
Joyci116 said:
(2x-x)(cosx)

Would you use the product rule after using the power rule and chain rule?
No. Use the product rule first. You don't need the chain rule at all.

(x2-x)cosx+sinx(2x-1)

X2cosx-xcosx+2xsinx-sinx

That's more like it!

## 1. What is the concept of finding the derivative?

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.

## 2. Why is finding the derivative important?

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.

## 3. How is the derivative calculated?

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.

## 4. Can the derivative of a function be negative?

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.

## 5. What are some applications of finding the derivative?

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.

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