百度试题 结果1 题目Prove, from first principles,that the derivative of x3 is 3x2. 相关知识点: 试题来源: 解析 cu shi bai qin huan zhuang feng xuxuán 反馈 收藏
Verify the formula for the derivative of csc x = 1/sin x. Prove that the derivative of sec x is sec x tan x. 1. Use the definition of derivative to prove \lim_{n \rightarrow 2} f(x) = 4 given f(x) = x^2 -9 . 2. Suppose that G(x) = (g \cdot f)_{(x)} and H...
Use the definition of derivative to prove the following statement: a) f(x) = sin(x) ⇒ f'(x) = cos(x) b) f(x)= cos(x) ⇒ f'(x) = -sin(x) Use the definition of the derivative to find the derivative of f(x) = x^2 + \cos 5x. ...
g′(x)=11+x2 Step 5: Find the derivative of f with respect to gWe need to find:f′(x)g′(x)=12⋅11+x211+x2=12 ConclusionSince f′(x)g′(x)=12, which is a constant, we conclude that the derivative of f(x) with respect to g(x) is independent of x. Show More ...
Step 1: Differentiate f(x)We start with the function:f(x)=αxnWe need to find the derivative f′(x) with respect to x. Step 2: Apply the power ruleUsing the power rule of differentiation, we differentiate f(x):f′(x)=α⋅ddx(xn)=α⋅nxn−1So, we have:f′(x)=αnxn...
The well-known derivative ln(x) is one that students often find easy to memorize due to many real-life applications. Learn the step-by-step process used to solve the derivative and the application of the derivative of ln(x) using a real-world example. ...
The derivative of a function {eq}f(x) {/eq} is defined as the limit when the increment goes to 0 of the incremental quotient {eq}\dfrac{\Delta f}{\Delta h} {/eq}. In mathematical terms, {eq}\dfrac{df}{dx}= \displaystyle \lim_{\Delta h \to 0} \dfrac{f(x+\Delta h) -f...
Use the limit definition of the derivative to prove the followingspecial case of the Product Rule:d/(dx)(xf(x))=xf'(x)+f(x) 相关知识点: 试题来源: 解析 d/(dx)(xf(x))=lim_(h→0)((x+h)f(x+h)-f(x))/ =lim_(h→0)(x(f(x+h)-f(x))/h+f(x+h)) =xlim_(h→0)(...
Choulli, M., Henrot, A.: Use of the domain derivative to prove symmetry results in partial differential equations. Math. Nachr. 192, 91-103 (1998)Choulli, M., Henrot, A.: Use of the domain derivative to prove symmetry results in partial differential equations. Math. Nachr. 192 , 91...
Homework Statement A function f(x) has a periodic derivative. In other words f ' (x + p) = f ' (x) for some real value of p. Is f(x) necessarily...