Question

4 the order derivative of sinx
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Answer 1

It is no use saying sometimes it is sin(x) and sometimes cos(x) but since

cos(x) = sin(x + 90) I thought it would make sense to change all the derivatives

to sin(x + a number of 90 degrees)

The pattern works out beautifully!

If y = sin(x)

1st deriv = cos(x) = sin(x + 90)

2nd deriv = – sin(x) = sin(x + 2×90)

3rd deriv = – cos(x) = sin(x + 3×90)

4th deriv = sin(x) = sin(x + 4×90)

5th deriv = cos(x)= sin(x + 5×90)

6th deriv = – sin(x)= sin(x + 6×90)

7th deriv = – cos(x) = sin(x + 7×90)

so obviously the nth derivative must be:

nth deriv = sin(x + 90n)