Question

plss answer this and explain to me
Derivatives of trigonometric functions

Answer 1

well, a derivative of sinx is -cosx, and the derivative of cosx is sinx

Answer 2

\[y=\sin ^{2}(\frac{ 3 }{ x ^{2} })\]

Answer 3

Find the derivative of the inside function, then the outside function, and multiply them together. What did you learn in class about derivatives?

Answer 4

its like a chain rule
derivative of outside times the derivative of the inside, then keep the inside of the sine the same

Answer 5

plss show the solution so i can understand it

Answer 6

Start from the outside and move in.

You can view

\[y = \sin^2(3/x^2)\]

as
\[y = (\sin(3/x^2))^2\]

So we take the derivative of the outside but keep the stuff inside the brackets the same, which gives us

\[2\sin(3/x^2)\]

Then, due to the chain rule, we multiply this by the derivative of the next part in, which is the sine. This gives us:

\[2\sin(3/x^2)*\cos(3/x^2)\]

And finally, one more use of the chain rule has us multiplying this by the derivative of 3/x^2. This gives us:

\[2\sin(3/x^2)*\cos(3/x^2)*(3*(-2)/x^3)\]