"Wolfram's Derivative of (sin x)^2: Is it Correct?

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In summary, Wolfram says the derivative of (sin x)^2 is sin2x, but it can also be written as 2(sin x)(cos x). These are the same because of the double angle formula for sine. Trigonometry can be frustrating, but it is important to understand for physics and math. The identities may feel synthetic, but they are there to help. Some identities can be derived using Euler's formula.
  • #1
1MileCrash
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Homework Statement



Wolfram says the derivative of (sin x)^2 is sin2x. Shouldn't it be 2(sin x)(cos x)?
 
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  • #2
Are these results different?
 
  • #3
...apparently.

Why on Earth is that? Which of the umpteen trigonometric identities?
 
  • #4
1MileCrash said:

Homework Statement



Wolfram says the derivative of (sin x)^2 is sin2x. Shouldn't it be 2(sin x)(cos x)?

They are the same. This is the double angle formula for sine.
 
  • #5
sin(2x) = 2 sin(x) cos(x)

You can get this from sin(2x) = sin(x + x)
= sin(x) cos(x) + cos(x) sin(x)

= 2 sin(x) cos(x)​
 
  • #6
Trigonometry really pisses me off sometimes.
 
  • #7
If you're working toward a degree in physics and/or math, you had better get a solid handle on trig.
 
  • #8
I like using it for things like vectors, I just don't like the identities. They feel "synthetic."
 
  • #9
1MileCrash said:
I like using it for things like vectors, I just don't like the identities. They feel "synthetic."
Synthetic?

The identities are there to help you out. In your other current post, you put in a lot more work than was necessary, by not using a fairly simple identity: cos(2x) = cos2(x) - sin2(x).
 
  • #10
these identities can be derived using Eulers formula.
 

FAQ: "Wolfram's Derivative of (sin x)^2: Is it Correct?

What is Wolfram's Derivative of (sin x)^2?

Wolfram's Derivative of (sin x)^2 is the mathematical expression for finding the derivative of the function (sin x)^2, also known as the derivative function.

How is Wolfram's Derivative of (sin x)^2 calculated?

Wolfram's Derivative of (sin x)^2 is calculated using the power rule, which states that the derivative of x^n is n*x^(n-1). In this case, the derivative of (sin x)^2 is 2*(sin x)^(2-1) = 2*sin x.

Is Wolfram's Derivative of (sin x)^2 different from other derivative formulas?

No, Wolfram's Derivative of (sin x)^2 follows the same rules and principles as other derivative formulas. It is simply a specific expression for finding the derivative of (sin x)^2.

Why is the derivative of (sin x)^2 important?

The derivative of (sin x)^2 is important because it allows us to calculate the rate of change of the function (sin x)^2 at any given point. This can be useful in many applications, such as physics, engineering, and economics.

Can Wolfram's Derivative of (sin x)^2 be used for any value of x?

Yes, Wolfram's Derivative of (sin x)^2 can be used for any value of x, as long as the function (sin x)^2 is defined at that point. However, the derivative may not exist at certain values of x, such as at x = pi/2, where the function has a vertical tangent line.

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