Weby ″ + y = xexcos(x) (D2 + 1)y = xexcos(x) Now firstly we have to find C.F A.E is m2 + 1 = 0 & m = + i, − i Hence C. F = c1sinx + c2cosx Now we have to calculate P.I = ( 1 D2 + 1)xexcos(x) = ex( 1 ( D + 1)2 + 1)xcos(x) = ex( 1 D2 + 1 + 2D)xcos(x) = ex. x( 1 f ( D))cos(x) - ex( 1 f ( D)2)[f ′ (D)cos(x) = ex. xsinx − exsinx Hence complete solution is WebQuestion: Find the second derivative of the function f(x)=xcosx. Select one: a. −xcosx+x22sinx−x32cosx b. −xcosx+x22sinx+x32cosx c. xcosx+x22sinx−x32cosx d. −xcosx−x22sinx+x32cosx e. xcosx+x22sinx+x32cosx. Show transcribed image text. Expert Answer. Who are the experts?
Antiderivative Calculator - Symbolab
WebFind the derivative of sin x cos x. Let, y = sin x cos x. Differentiate both sides w.r.t x, using product rule. d y d x = d d x sin x cos x = sin x d d x cos x + cos x d d x sin x ... WebFeb 26, 2015 · Calculus Differentiating Trigonometric Functions Intuitive Approach to the derivative of y=sin (x) 1 Answer Michael Feb 26, 2015 y' = xcosx Use the product rule for d (xsinx) dx: (uv)' = u dv dx +v du dx Where u = x and v = sinx So d(xsinx) dx = xcosx + sinx dx dx = xcosx +sinx Now d(cosx) dx = −sinx So combining the 2 we get: hull city v barnsley fc
Derivative of cos x - Formula, Proof, Examples - Cuemath
WebHence, the antiderivative of xcosx is the same as the integral of xcosx. Why is the Integral of xcosx Equal to xsinx + cosx + C? The integral of xcosx is equal to xsinx + cosx + C … WebJul 19, 2024 · Explanation: As the derivative is linear: df dx = d dx (xcosx) − d dx (sinx) = d dx (xcosx) −cosx. applying now the product rule: df dx = x d dx (cosx) +( d dx x)cosx − … WebThe derivative of cos(x) cos ( x) with respect to x x is −sin(x) - sin ( x). 2(sin(x)(−sin(x))+cos(x) d dx [sin(x)]) 2 ( sin ( x) ( - sin ( x)) + cos ( x) d d x [ sin ( x)]) Raise sin(x) sin ( x) to the power of 1 1. 2(−(sin1 (x)sin(x))+cos(x) d dx [sin(x)]) 2 ( - ( sin 1 ( x) sin ( x)) + cos ( x) d d x [ sin ( x)]) hull city v burnley