Differentiate using the Product Rule which states that ( d/(du)[f(u)g(u)]) is ( f(u)d/(du)[g(u)]+g(u)d/(du)[f(u)]) where ( f(u)=u-√u) and ( g(u)=u+√u). ( (u-√u)d/(du)[u+√u]+(u+√u)d/(du)[u-√u]) Differentiate. ( (u-√u)(1+d/(du)...
Differentiate using the Product Rule which states that ( d/(dy)[f(y)g(y)]) is ( f(y)d/(dy)[g(y)]+g(y)d/(dy)[f(y)]) where ( f(y)=e^y) and ( g(y)=y^e).( e^yd/(dy)[y^e]+y^ed/(dy)[e^y])Differentiate using the Power Rule which states that ( d/(dy)...
Letf(x)=(x3+2x−7)(3+x−x2). We compute the derivative using the product rule. Recall thatddx[xn]=nxn−1. We then... Learn more about this topic: Product Rule in Calculus | Overview, Equations & Examples from Chapter 10/ Lesson 14 ...
Differentiate using the Product Rule which states that ( d/(dr)[f(r)g(r)]) is ( f(r)d/(dr)[g(r)]+g(r)d/(dr)[f(r)]) where ( f(r)=(d^2)/(dr^2)) and ( g(r)=π r^2). ( (d^2)/(dr^2)d/(dr)[π r^2]+π r^2d/(dr)[(d^2)/(dr^2)]) Differentiate...
Chain Rule (usingddx)dydx=dydududx "The derivative of" is also writtenddx Soddxsin(x)andsin(x)’both mean "The derivative of sin(x)" Examples Example: what is the derivative of sin(x) ? From the table above it is listed as beingcos(x) ...
The rules of differentiation are useful to find solutions to standard differential equations. Identify the application of product rule, quotient rule, and chain rule to solving these equations through examples. Related to this QuestionFind the derivative using the Chain Rule. y = e9x (...
Usingproduct ruleon the left side, x d/dx(y) + y d/dx(x) = d/dx(5) x (dy/dx) + y (1) = 0 x(dy/dx) = -y dy/dx = -y/x From xy = 5, we can write y = 5/x. dy/dx = -(5/x)/x = -5/x2 In Method -1, we have converted the implicit function into the ...
Using the product rule: f′(x)=ddx[sin(x)]⋅ex+sin(x)⋅ddx[ex]=cos(x)⋅ex+sin(x)⋅ex=ex(cos(x)+sin(x)) 2. Partial Derivative Partial derivatives extend the concept of derivatives to functions of multiple variables. They measure the rate of change of...
Discovering Derivatives and Derivative Rules including Product, Quotient and Chain RuleWildstrom, Susan Schwartz
百度试题 结果1 题目Use the Product Rule to compute the derivative:()()((t^2+1)(t+9))∣_(t=-4) = ___ 相关知识点: 试题来源: 解析 -23 反馈 收藏