\lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More

Why does the value $-\ln(|\cos(x)|)$ become $\ln(|\sec(x)|)?$ I was doing an integral and I got my final answer as that, but I don't understand how you can just send the negative sign inside and m...

2017年4月1日 · How do you find the derivative of y = ln(sec x)? In order to differentiate this function, we must use the chain rule: (f g(x))' = f '(g(x)) × g'(x). Informally, this means that if we have to derivate a composite function, f g(x), then we differentiate f with respect to x, treating g(x) as if it were x and then multiply that derivative by g'(x).

2015年3月26日 · 1/【 (seca+tana)* (sina*cosa)^2】。 直接算就可以了，seca=1/cosa,tana=sina/cosa。 注我打不出阿尔法，用a代替。 ^_^

Now let’s use the chain rule to take the derivative of ln(sec x)). Oddly enough, this strange looking function is not only interesting as a review of the chain rule. The natural log was invented before the exponential function by a man named Napier, exactly in order to evaluate functions like this.

2014年1月6日 · \ln { (\sec {x})} ln(secx) 的導數？ 看看下面的答案！ \frac {d} {dx} \ln { (\sec {x})} dxd ln(secx) 上使用 連鎖法則。 u=\sec {x} u = secx。 \sec {x}\tan {x} secxtanx。 \"本週的數學 …

2020年8月29日 · -------------------------------- These animations are largely made using manim, a open-source python library: https://github.com/3b1b/manim #integralof #derivatives #calculus. …

Why is −ln(cos(x)) equal to ln(sec(x))? You have a^b = c \iff b = \log_a (c). Use this to show that for any power r, \log_b (a^r) = r\log_b (a) for any base b. You have ab = c b = loga(c). Use this to show that for any power r, logb(ar) = rlogb(a) for any base b.

记忆技巧：正弦正切正割求导后的函数都是正的，余弦余切余割求导后的函数都是负的。 (\tan x)' = (\frac {\sin x} {\cos x})' \\ = \frac { (\sin x)'\cos x - \sin x (\cos x)'} {\cos^2 x} \\ = \frac {\cos^2 x + \sin^2 x} {\cos^2 x} \\ = \frac { 1 } {\cos^2 x} \\ = \sec^2 x.

\begin{align} (ln(secx+tanx))' &=\frac{1}{secx+tanx}(secx+tanx)'\\ &=\frac{1}{secx+tanx}(sec^{2}x+secx\ tanx)\\ &=secx(\frac{secx+tanx}{secx+tanx})\\ &=secx \end{align}