It's not true because the derivative of sine is not itselfmattmns said:Is the derivative of sin(3x) just 3sin(3x) because of the chain rule? IE, let u=3x, then 3sin(u) => 3sin(3x)
Thanks.
Ok, I am pretty sure that is true. How about, [tex]
\lim_{t\rightarrow 0} tln(t)
[/tex]
What is the common approach for this problem?
The derivative of sin(3x) is 3cos(3x).
To find the derivative of sin(3x), you can use the chain rule. First, take the derivative of the outer function sin(x), which is cos(x). Then, multiply by the derivative of the inner function (3x), which is 3. This results in 3cos(3x).
The derivative of sin(x) is cos(x), so when we apply the chain rule to sin(3x), we get 3cos(3x) as the derivative. This is because the 3 in front of the x is considered a constant, and the derivative of a constant is 0, leaving us with just cos(3x).
The graph of the derivative of sin(3x) is a cosine curve with a period of 2π/3 and an amplitude of 3. It intersects the x-axis at every multiple of 2π/3 and the y-axis at (0,3).
The derivative of sin(3x) has many applications in physics, engineering, and other scientific fields. It can be used to model the motion of a spring, the behavior of sound waves, and the analysis of electrical circuits, among other things.