Find the derivative and differential of the function y = sin (√2 / x).
| July 25, 2021 | education
The derivative of a complex function is
(sin u) ‘= cos u * u’.
The derivative of the function y = sin ((2 ^ 1/2) / x):
y ‘= sin ((2 ^ 1/2) / x)’ = cos ((2 ^ 1/2) / x) * ((2 ^ 1/2) / x) ‘= cos ((2 ^ 1 / 2) / x) * (2 ^ 1/2) * (x ^ (- 1)) ‘= 2 ^ 1/2 * cos ((2 ^ 1/2) / x) * (-1) * (x ^ (- 2)) = -cos ((2 ^ 1/2) / x) * (2 ^ 1/2 / x ^ 2).
The differential of a complex function is
dy = (sin u) ‘dx = cos u * u’ dx.
For this function:
dy = y ‘dx = -cos ((2 ^ 1/2) / x) * (2 ^ 1/2 / x ^ 2) dx.
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