Derivatives of Trigonometric Function

[PMC_l0ver]

Homework Statement

find the dy/dx

of y = Sin⁴ x² - Cos⁴ x²

Homework Equations

derivatives and identities
factoring

dy/dx (Sinx) = Cosx
dy/dx (Cosx) = -Sinx

The Attempt at a Solution

y = (Sin² x² - Cos² x²) (Sin² x² + Cos² x²)

im stuck at this part i don't know how to get to the next step
which suppose to be " y = -(Cos² x² - Sin² x²) " base on the book

then that would equal to -Cos2x²
therefore the answer for dy/dx = Sin2x²(4x)
= 4x Sin2x²

please explain this to me

 

[micromass]

Try to use the following formula's

$$\cos^2(\alpha)+\sin^2(\alpha)=1$$

and

$$\cos^2(\alpha)-\sin^2(\alpha)=\cos(2\alpha)$$

That will simplify a bit...

 

[PMC_l0ver]

ohh ok thank you! i got it