Approximate value of ln0.99 by differential

Approximate value of ln0.99 by differential

The derivative of LNX is 1 / X
According to the meaning of derivative, when Δ x is very small, it can be obtained approximately
f(x+Δx)=f(x)+f'(x)Δx.
Let x = 1, Δ x = - 0.01
The approximate value of ln0.99 is -0.01

Transformation of trigonometric function in a differential
∫ [1 / (Tan ^ 2 T * sec T)] * [1 / cos ^ 2 T] * DT equals?
My foundation is poor, do not understand the trigonometric function formula used in the conversion. Excellent additional integral

Sect = 1 / cost, (sect) ^ 2 = 1 + (tant) ^ 2csct = 1 / Sint, (CSCT) ^ 2 = 1 + (Cott) ^ 2, Cott is the cotangent of ∫ [1 / (Tan ^ 2 T * sec T)] * [1 / cos ^ 2 t] * DT = ∫ cost / (Sint) ^ 2 DT = ∫ 1 / (Sint) ^ 2 dsint = - 1 / Sint + C

Differential of trigonometric function
To find the differential of sin ^ 2 (3x) DX, I am a big mathematician
Wrong, indefinite integral
The original formula is to reduce the power

sin^2(3x)=（1-2cos（6x））/2
So = x / 2-sin (6x) / 6 + C