Question

How do I find the derivative of `y = sin^2 x + cos^2x + ln(e^x)`?

Answer 1

Derivatives of `y=sin^2x+cos^2x+ln(e^x)` can be easily find by finding the derivative for each component as the derivative of the sum is the sum of the derivative.

Derivative of `sin^2x` is `2sin(x) * d(sin(x)) = 2sin(x)cos(x)`
Derivative of `cos^2x` is `2cos(x) * d(cos(x)) = -2cos(x)sin(x)`
Derivative of `ln(e^x)` is `1/e^x * d(e^x) = 1/e^x*e^x = 1` [*]

Note [*] that the last component `ln(e^x)` is actually `x`. Therefore, the derivative of `x` is actually `1`.