Generally, the derivative of sine is cosine.
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Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x
You are supposed to use the chain rule for this. First step: derivative of root of sin2x is (1 / (2 root of sin 2x)) times the derivative of sin 2x. Second step: derivative of sin 2x is cos 2x times the derivative of 2x. Third step: derivative of 2x is 2. Finally, you need to multiply all the parts together.
The derivative of sin(x) is cos(x). Coefficients act like constants and always remain in derivatives. So, the derivative is -2cos(x).
Since 8 is a constant, you can use the rule for constants.In other words, the derivative is 8 times the derivative of cos x.
y = -2sin2x y' = (2)(-2cos2x) = -4cos2x *derivative of sin is cos *multiply by 2 because of chain rule