\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

2020年12月2日 · 是不是想表达x趋于0时，lncosx等价于cosx-1. 直接用 等价无穷小 替换即可。 已知 ln(1+x)\\sim x. 故有 ln(1+cosx-1)\\sim cosx-1

∫ln(cosx)dx 区间(0 π/2) 利用区间再现公式. ∫lncosxdx=∫lncos(π/2-x)dx=∫lnsinxdx

2014年8月22日 · You can find this derivative by applying the Chain Rule, with #cosx# as the inner function, and #lnx# as the outer function. Process: To apply the chain rule, we first find the derivative of the outer function, #lnu#, with #u = cosx#. …

2015年10月16日 · What is the derivative of ln(cos x)? Trevor Ryan. Rule : d dx lnu(x) = 1 u ⋅ du dx. ∴ d dx ln(cosx) = 1 cosx ⋅ d dx cosx. = 1 cosx ⋅ − sinx. = − sinx cosx. = − tanx.

https://socratic.org/questions/how-do-you-use-the-chain-rule-to-differentiate-ln-cosx \displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\ln{{\left(-{\cos{{x}}}\right)}}}=-{\tan{{x}}} Explanation: The Chain Rule, when applied to logarithms, tells us that \displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\ln{{\left({u}\right)}}}=\frac{{1}}{{\ln{{u ...

\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} 显示更多

Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…

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.

具体回答如下：积分限分为0到π/4，π/4到π/2。 π/4到π/2上的积分换元x=π/4-t，化为lncosx 从0到π/4的积分。 原式=∫（0到π/4） （lnsinx+lncosx）dx=∫.