# Compute the following derivatives

• Torshi
In summary, the conversation is about computing derivatives using the product rule and quotient rule, without using the chain rule. The problem involves finding the derivative of (sin(x))^2. The attempt at a solution shows the use of the product rule to get the final answer of 2(sin(x))(cos(x)), which is equivalent to sin(2x).
Torshi

## Homework Statement

compute the following derivatives using the product rule and quotient rule as necessary, without using chain rule.

## Homework Equations

d/dx ((sin(x))^2)

## The Attempt at a Solution

=(sin(x))(sin(x))
=(cos(x))(sin(x))+(sin(x))(cos(x))
=2(sin(x))(cos(x))

Torshi said:

## Homework Statement

compute the following derivatives using the product rule and quotient rule as necessary, without using chain rule.

## Homework Equations

d/dx ((sin(x))^2)

## The Attempt at a Solution

=(sin(x))(sin(x))
=(cos(x))(sin(x))+(sin(x))(cos(x))
=2(sin(x))(cos(x))
Looks fine to me. The final answer is equivalent to sin(2x) [trig identity] in case you want a slightly simpler form.

jbunniii said:
Looks fine to me. The final answer is equivalent to sin(2x) [trig identity] in case you want a slightly simpler form.

Thanks

## 1. What is the purpose of computing derivatives in science?

Computing derivatives allows scientists to analyze and understand the rate of change of a function or system. It is a powerful tool in various fields of science, such as physics, economics, and engineering, as it helps in predicting and optimizing outcomes.

## 2. How do you compute derivatives?

The most common method for computing derivatives is using the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of a function by manipulating its algebraic expression.

## 3. Why is it important to know the derivatives of a function?

Knowing the derivatives of a function allows us to determine the slope of the function at any point and understand its behavior. This information is useful in various scientific applications, such as predicting the motion of an object, finding maximum or minimum values, and analyzing the stability of a system.

## 4. Can derivatives be used to solve real-world problems?

Yes, derivatives have numerous real-world applications, including optimization problems in economics, mechanics, and engineering. They can also be used to model and analyze natural phenomena, such as population growth, chemical reactions, and weather patterns.

## 5. Are there any limitations to computing derivatives?

Yes, there are some limitations to computing derivatives, such as when the function is not differentiable or when the calculations become too complex. In these cases, alternative methods, such as numerical differentiation, may be used to approximate the derivative.

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