Finding the derivative of a function is called differentiation. Basically, you calculate the slope of the line that goes throughfat the pointsxandx+h. Because we take the limit forhto 0, these points will lie infinitesimally close together; therefore, it is the slope of the function in the...
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\(v^\prime=\cos x\),所以\(y^\prime = 2x\sin x+x^{2}\cos x\)。选项B中符...
The derivative of a function, f'(x) can be interpreted as the slope of the tangent line. Since the derivative is the slope of a tangent line it can be given as {eq}\displaystyle \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} {/eq}. We can use this definition to find the ...
Therefore, the derivative of a function can be found by differentiating that function. For example; the derivative of the function f(x)=x is f′(x)=1 and the derivative of the function f(x)=sinx is f′(x)=cosx and so on. Answer...
Find the functional derivative of the functional S[y]=∫aby(x)sin(y(x))dx with respect to the function y, where the integrand is f[y(x)]=y(x)sin(y(x)). Declare y(x) as a symbolic function and define f as the integrand of S. Use f and y as the parameters of functionalDer...
Answer to: Consider the following derivative of a function: f'(x) = x^{-5/7} (x+5). At what points, if any, does the function assume local maximum...
A function of any angle is equal to the cofunction of its complement. (Topic 3 of Trigonometry).Therefore, on applying the chain rule:We have established the formula.The derivative of tan xd dx tan x = sec2x Now, tan x = sin x cos x . (Topic 20 of Trigonometry.)...
Find the derivatives of the function sin ^(-1) sqrtx 01:58 Find the derivatives of the function tan ^(-1) (cos sqrtx) 01:58 Find the derivatives of the function sin (tan ^(-1) (e ^(x))) 02:17 Find the derivatives of the function (cot ^(-1) x ^(3)) ^(2) 02:13 Fin...
结果1 题目 The first derivative of the function f is given by f'(x)=sin (x^2). At which of the following values of x does f have a local minimum? () A. 2.507 B. 2.171 C. 1.772 D. 1.253 E. 0 相关知识点: 试题来源: 解析 A 反馈 收藏 ...
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