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