sin(x2)is made up ofsin()andx2: f(g) = sin(g) g(x) = x2 The Chain Rule says: the derivative of f(g(x)) = f'(g(x))g'(x) The individual derivatives are: f'(g) = cos(g) g'(x) = 2x So: ddxsin(x2) = cos(g(x)) (2x) ...
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The derivative of cos x. sin x can be calculated using the product rule of differentiation. d(cos x. sin x)/dx = (cos x)' sin x + cos x (sin x)' = -sin x.sin x + cos x. cos x = cos2x - sin2x = cos 2x. Hence, the derivative of cos x.sin x = cos 2x What is ...
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...
What is the derivative of (sec(x)/(1+tan(x))) ? The derivative of (sec(x)/(1+tan(x))) is (-cos(x)+sin(x))/(1+sin(2x)) What is the first derivative of (sec(x)/(1+tan(x))) ? The first derivative of (sec(x)/(1+tan(x))) is (-cos(x)+sin(x))/(1+sin(2x...
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Find the derivative of cos x from first principle. 03:03 Find the derivative of the following functions: (i) sin x cos x (ii... 04:05 Find the derivative of (i) 2x-3/4 (ii) (5x^3+3x-1)(x-1) (iii) ... 03:29 Find the derivative of (x^n-a^n)/(x-a)for some consta...
Question: Find the derivative: f(x)=sec2xsecx2. Product Rule: Recall that we use the product rule to compute the derivative of a function that can be written as the product of two functions. It is [fg]′=f′g+fg′ But what if we have a triple product, or even more? No worries...
tanx=sinxcosx cotx=cosxsinx 3)cscx=1sinx,among others. Answer and Explanation:1 Let us find the derivative ofy=sec(x). Let's redefine the function as a function of cosine. Thus we have {eq}y = \dfrac{1}{\cos x}... ...
What is the derivative of y = (e^(-x^2))(ln(tan x))? What is the derivative of ln(sinh x)? What is the derivative of y^2(6-2x)? What is the derivative of x^{\sin(\frac{\pi}{4})}? What is the derivative of y= xcos(x)sin(x) ?