10:[["$","title","0",{"children":"CUET Mathematics - d^2/dx^2\\de^x[x^3/2 - e^x]\\ equals | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The given expression is d^2/dx^2\\e^x[x^3/2 - e^x]\\ Expand the expression inside: f(x) = e^x x^3/2 - e^x e^x f(x) = x^3e^x/2 - e^2x

For the first derivative, differentiate f(x) = x^3e^x/2 - e^2x For the first term, using the product ru<= with u = x^3 and v = e^x: d/dx(x^3e^x/2) = 1/2[(3x^2)(e^x) + (x^3)(e^x)] = e^x/2(3x^2 + x^3) For the second term: d/dx(e^2x) = 2e^2x Therefore: f'(x) = e^x/2(x^3 + 3x^2) - 2e^2x

For the second derivative, differentiate f'(x) = e^x/2(x^3 + 3x^2) - 2e^2x For the first term, using the product ru<=: d/dx[e^x/2(x^3 + 3x^2)] = 1/2[e^x(x^3 + 3x^2) + e^x(3x^2 + 6x)] = e^x/2(x^3 + 3x^2 + 3x^2 + 6x) = e^x/2(x^3 + 6x^2 + 6x) = xe^x/2(x^2 + 6x + 6) For the second term: d/dx(2e^2x) = 4e^2x Therefore: f''(x) = xe^x/2(x^2 + 6x + 6) - 4e^2x"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Continuity & Differentiability"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - d^2/dx^2\\de^x[x^3/2 - e^x]\\ equals | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The given expression is d^2/dx^2\\e^x[x^3/2 - e^x]\\ Expand the expression inside: f(x) = e^x x^3/2 - e^x e^x f(x) = x^3e^x/2 - e^2x

For the second derivative, differentiate f'(x) = e^x/2(x^3 + 3x^2) - 2e^2x For the first term, using the product ru<=: d/dx[e^x/2(x^3 + 3x^2)] = 1/2[e^x(x^3 + 3x^2) + e^x(3x^2 + 6x)] = e^x/2(x^3 + 3x^2 + 3x^2 + 6x) = e^x/2(x^3 + 6x^2 + 6x) = xe^x/2(x^2 + 6x + 6) For the second term: d/dx(2e^2x) = 4e^2x Therefore: f''(x) = xe^x/2(x^2 + 6x + 6) - 4e^2x"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-15/18"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - d^2/dx^2\\de^x[x^3/2 - e^x]\\ equals | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The given expression is d^2/dx^2\\e^x[x^3/2 - e^x]\\ Expand the expression inside: f(x) = e^x x^3/2 - e^x e^x f(x) = x^3e^x/2 - e^2x

CUET Mathematics 2025 29 May Shift 2 PYQs

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