用implicit differentiation求得:y’ = 1/cos y 精彩部分:进一步转化为:y’ = 1/√[1-(sin y)^2] 而sin y = x,因此,(sin y)^2 = x^2, 解出:y’ = 1/√(1-x^2) 书本内容: 第一,书本对反函数进行了进一步的解释(补充高中知识欠缺的我)。 Theorem 5.6 Reflective property of inverse functi...
f(x+Δx)−f(x)Δx=sinΔx2Δx2cos(x+Δx2)⇒limΔx→0sinΔx2Δx2cos(x+Δx2)=1×cosx=cosxf(x+Δx)−f(x)Δx=sinΔx2Δx2cos(x+Δx2)⇒limΔx→0sinΔx2Δx2cos(x+Δx2)=1×cosx=cosx[Since cos x is continuous and ...
Here they are: y = f(x) dy/dx 1 xn nxn-1 2 ex ex 3 ekx kekx 4 ax ax.ln a 5 ln x 1/x 6 log ax 1/x ln a 7 sin x cos x 8 cos x - sin x 9 tan x sec2 x 10 cot x - cosec2 x 11 sec x sec x.tan x 12 cosec x - cosec x. cot x 13 sinh x cosh x...
TheGroupwillcontinuetoimplementthestrategiesofdifferentiationandcostleadershipinthesecond halfoftheyear,seekingtopursuestabledevelopmentanddeliversoundresultsbyenhancingprojectbasedoperationsandextendingitsadvantagesincostandtechnologyaswellasitsabilityinone-stop project delivery. ...
g_{2}'(0)=\lim_{x \rightarrow 0}{\frac{ g_{2}(x)}{x}}=\lim_{x \rightarrow 0}x\sin\frac{1}{x}=0 ,但在0以外的点,导数公式为cos(1/x) + 2x sin(1/x),这意味着在0的时候, g'_{2} 并不连续。所以g2的性质是这样的:连续、可微,但其导数在0不连续。 接下来我们试图用一...
symsstf = sin(s*t); Find the partial derivative∂f/∂tby usingdiffand specifying the variable to differentiate ast. Get Df_t = diff(f,t) Df_t =s cos(s t) To differentiatefwith respect to the variables, specify the variable to differentiate ass. ...
f. y′ = 2xcos(x2) g. y= (sinx)2⟹y′ = 2 sinxcosx= sin 2x h. y′ = etanxsec2x i. Example 2: What is the equation of the tangent line to the curvey=exInxat the point (1, 0)? The first step is to find the slope of the tangent line atx= 1, which is the value...
Given below are some more formulae of some logarithmic and trigonometric functions:d/dx (xx) = xx (1 + ln x) d/dx (logax) = 1/ x ln a d/dx (loga f(x)) = 1/ f(x) ln a . d/dx f(x) d/dx (sin x) = (sin x)' = cos x (cos x)' = -sin x (tan x)' = ...
d dx (U/V) = [V dUdx - U dVdx ]/ V2 Other Functions Differentiation of trigonometric and other functions f(x)f '(x) x 1 1/x -1/x2 exp(x) exp(x) exp(ax) a exp(ax) cos(x) -sin(x) sin(x) cos(x) tan(x) sec2(x) cosec(x) -cot(x)cosec(x) ln(x) 1/xSp...
TheGroupwillcontinuetoimplementthestrategiesofdifferentiationandcostleadershipinthesecond halfoftheyear,seekingtopursuestabledevelopmentanddeliversoundresultsbyenhancingprojectbasedoperationsandextendingitsadvantagesincostandtechnologyaswellasitsabilityinone-stop project delivery. ...