What is the derivative of y=cos^4(t)-sin^4(t) ?

The derivative of y=cos^4(t)-sin^4(t) is -sin(2t)*2

What is the first derivative of y=cos^4(t)-sin^4(t) ?

The first derivative of y=cos^4(t)-sin^4(t) is -sin(2t)*2

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derivative of

y = cos^{4} (t) - sin^{4} (t)

- sin (2 t) \cdot 2

Solution steps

\frac{d}{d t} (cos^{4} (t) - sin^{4} (t))

Simplify

cos^{4} (t) - sin^{4} (t) : cos (2 t)

= \frac{d}{d t} (cos (2 t))

Apply the chain rule:

- sin (2 t) \frac{d}{d t} (2 t)

= - sin (2 t) \frac{d}{d t} (2 t)

\frac{d}{d t} (2 t) = 2

= - sin (2 t) \cdot 2

What is the derivative of y=cos^4(t)-sin^4(t) ?
The derivative of y=cos^4(t)-sin^4(t) is -sin(2t)*2
What is the first derivative of y=cos^4(t)-sin^4(t) ?
The first derivative of y=cos^4(t)-sin^4(t) is -sin(2t)*2