The product rule tells us the derivative of two functions f and g that are multiplied together ... (fg) = fg gf ... (The little mark means derivative of.)
When differentiating a product, each factor is differentiated, but one at a time. You can think of this as "each factor gets a turn at being the derivative." This pattern holds true, even when there are more than two factors in the product, as shown below. ...
Answer to: Use the product rule to find the derivative of y = (x + 1)(sqrt(x) + 2). By signing up, you'll get thousands of step-by-step solutions...
In this paper we extend the well known formula for the derivative of a product of real‐valued functions to the case in which one of the functions has range in a Banach space.EnriqueDepartmentA.DepartmentGonzalez‐VelascoDepartmentInformaworldInternational Journal of Mathematical Education in Science ...
In the problem,we have to use the product rule to find the derivative of {eq}\displaystyle f(x) = (x^2 + 2xe^x +1)(5x^3 - \frac{2}{x^2}) {/eq} As...Become a member and unlock all Study Answers Try it risk-free for 30 days Try it risk...
Use the product rule to find the derivative of the function. f(x)=(x3−3x)(3x2+2x) Product Rule: The product rule is associated with the operation of differentiation. This entails taking the derivative of the function that is expressed as a product of discrete ter...
Find the Derivative Using Product Rule - d/du h(u)=(u- square root of u)(u+ square root of u) ( h(u)=(u-√u)(u+√u)) 相关知识点: 试题来源: 解析 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...
So, product rule is OK for taking the derivative of a dot product.───那么乘积法则对点乘求导没问题。 then, dA, so we had to use the product rule carefully, or we use the partials.───那么对于dA,我们必须谨慎地使用乘法法则,或用偏微分。 Well, then, dA, so we had to use the pro...
When working with derivatives, rules such as addition and subtraction simply state that the derivative of an addition or subtraction is equal to the derivative of the individual parts added or subtracted. If this was true with the product rule, then the formula would be: ...
The derivative is \(2x\sin x - x^{2}\cos x\) 相关知识点: 试题来源: 解析 A。解析:对于函数\(y = uv\)(这里\(u = x^{2}\),\(v=\sin x\)),根据乘积法则\((uv)^\prime = u^\prime v+uv^\prime\)。\(u = x^{2}\)的导数\(u^\prime = 2x\),\(v=\sin x\)的导数\(...