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...其中derivative可以替换为differential...image.png derivative x^3+y^3-3a x y=0 with respect to x 执行后的结果显示为 ? image.png ? image.png ?...例2 计算以下函数指定方向的方向导数: 输入表达式为 derivative of f(x,y) in the direction (a,b) 执行后的结果显示为 ?
Calculate the derivative of the following function with respect to {eq}x {/eq}, and evaluate any remaining integrals. {eq}\displaystyle I(x) = \int_0^1 \dfrac {t^x - 1} {\ln (t)}\ dt {/eq} Definite Integrals: When...
Find the derivative of the function F(theta) = arcsin(sqrt sin(5theta)) with respect to theta. Find the derivative of y with respect to theta. y = sech^ {-1} (1 / 4)^ theta. Find the derivative of y with respect to theta of y=ln (sec (ln (9 theta))). Fin...
(b) Differentiate R with respect to q to find the marginal revenue, M R, in terms of q. Calculate the marginal revenue when q = 10. (c) Calculate the change in total revenue when produc- tion increases from q = 10 to q = 11 units. Confirm that a one unit increase in q gives ...
France E-mail: stefanos.katmadas@unimib.it, ruben.minasian@cea.fr Abstract: We consider the Calabi-Yau reduction of the Type IIA eight derivative one- loop stringy corrections focusing on the couplings of the four dimensional gravity multiplet with vector multiplets and a tensor multiplet containin...
The slope of a function is zero at a local maximum or minimum. Applications in Physics: Equations govern the motion of objects and their locations as a function of time. Velocity is a rate of change of position. Acceleration is the derivative of the velocity with respect to time....
Lie derivative of tensor field with respect to Lie bracket I'm trying to show that the lie derivative of a tensor field ##t## along a lie bracket ##[X,Y]## is given by \mathcal{L}_{[X,Y]}t=\mathcal{L}_{X}\mathcal{L}_{Y}t-\mathcal{L}_{Y}\mathcal{L}_{X}t but ...
Let us consider a function f(x). The rate of change of f(x) with respect to variable x is represented as f'(x). Chain Rule of Differentiation Chain rule in differentiation helps us to differentiate the complex functions. By using the Chain rule: d(cos(f(x)))dx=−sin(f(...
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