= 2x cos(x2)Another way of writing the Chain Rule is: dy dx = dy du du dx Let's do the previous example again using that formula:Example: What is d dx sin(x2) ? dy dx = dy du du dx Let u = x2, so y = sin(u): d dx sin(x2) = d du sin(u) d dx x2 Differe...
[Solved] Unwanted minus sign in this derivative of a circular curve y'(t)/x'(t) = cos t/-sin t = -cot t. But as t is the angle, and the derivative is the slope, then isn't the slope supposed to be tan t? nomadreid
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...
Find the first derivative of f(x) = (tan -1 x)ln(2x - 1) Find the first derivative of y = sec^{-1} (x^2) Find the first derivative of f(a) = \dfrac{\sqrt{a{a} Find the first derivative of: y = sin3(cos 2x). ...
The correct Answer is:(i)−xsinx+2cosx (ii)−e2x(5cos3x+12sin3x) (iii)(5x+6xlogx) To find the second derivative of the given functions, we will follow the steps of differentiation carefully for each part. Part (i): y=xsinx Step 1: First DerivativeUsing the product rule:dydx...
Find :∫sinx+cosx√sin2xdx View Solution ∫sinx+cosx√1+sin2xdx View Solution Evaluate:∫sinx−cosx√sin2xdx View Solution ∫sinx+cosx√1+sin2xdx. Evaluate:∫sinx+cosx√1−sin2xdx View Solution Evaluate:∫sinx+cosx√1−sin2xdx ...
derivative of sin6(x) Solution 6sin5(x)cos(x)Hide Steps Solution steps dxd(sin6(x)) Apply the chain rule:6(sin(x))5dxd(sin(x)) =6(sin(x))5dxd(sin(x)) dxd(sin(x))=cos(x) =6(sin(x))5cos(x) Simplify=6sin5(x)cos(x)...
f(x)=sec2xsecx2. 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′ ...
Find the total derivative of ##u## with respect to ##x## see attached below; the textbook i have has many errors... clearly ##f_x## is wrong messing up the whole working to solution...we ought to have; ##\frac {du}{dx}=(9x^2+2y)+(2x+8y)3=9x^2+2y+6x+24y=9x^2+6x...