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 14 cosh x sinh xdoi:10.1007/978-1-4615-9653-0_7K. A. Stroud...
Step 2: Take the derivative of tan x. 20sec2 x Tangent Rule Example 1: sinx cosxStep 1: Apply the product rule. d dx [ f( x )g( x ) ]=f( x ) d dx [ g( x ) ]+g( x ) d dx [ f( x ) ] d dx [ sin x cos x ] sin x d dx cos x+cosx d dx sin x St...
Differentiate cos³x with respect to x. Let y = cos³x Let u = cos x therefore y = u³ dy= 3u² du du= -sin x dx dy=du×dy dx dx du = -sin x × 3u² = -sin x × 3cos²x =-3cos²x sin x Revision Maths hierarchy navigation...
Evaluate differentiation of y with respect to x : y=5x+cosx View Solution Differentiatexsinxwith respect to 'x'. View Solution Differentiatesinxxwith respect to x. View Solution Differentiateesinxwit respect to cos x. View Solution Exams
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...
当x\neq 0 时利用链式法则来求导,得到: \begin{aligned}f^\prime(x) = 2x\sin\frac{1}{x}- \cos\frac{1}{x}\end{aligned}。 当x=0 时,不能利用链式法则,因为这个时候 \begin{aligned}\frac{1}{x}\end{aligned} 没定义,我们利用导数定义来计算: \begin{aligned}\lim\limits_{x\to 0}\frac...
Definitions ofsin xandcos xQUESTIONSProperties and derivatives of trigonometric functionsPolar coordinatesQUESTIONSThe exponential functionsaxand the logarithmic functionslogax, and their derivatives. A. The functionsaxB. The funCalculus:The Elements
d/dx (sin x) = (sin x)' = cos x (cos x)' = -sin x (tan x)' = sec2 x (sec x)' = sec x tan x (cosec x)' = -cosec x cot x (cot x)' = -cosec2xSteps of Logarithm DifferentiationLogarithm Differentiation is the shortcut which helps in differentiating without using the...
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...
जो वास्तविक मान के साथ(−π2,π2)पर परिभाषित हो तथा जिसका पूर्वगF(x)इस प्रकार है किf(x)+cosx.F(x)=sin2x(1+sinx)2है...