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Calculus grade 12

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Determine the derivative of each function

A1) y = e^x(Sin²x)
A2) y = e²Sin²x
B1) y = (x³ + 1)e^-2
B2) y = (x² + 1)e^-2
C) y = x²(theta^Sinx)

  • Calculus grade 12 -

    I am not going to do all these
    if y = u(x) v(x)
    then dy/dx = u dv/dx + v du/dx
    for A1
    u = e^x so du/dx = e^x
    v = sin^2 x so dv/dx = 2 sin x cos x

    so
    dy/dx = 2e^x sin x cos x + e^x sin^2 x
    = e^x sin x ( 2 cos x + sin x)

  • Calculus grade 12 -

    Could you help me for these two:

    b) y = (x²+1)e^-4
    c) y = x²(e^Sinx)

    Please & Thank you.

  • Calculus grade 12 -

    e^-4 is a constant
    so
    e^-4(2x)

    x^2 d/dx (e^sin x) + 2 x e^sin x

    x^2 (e^sin x)cos x + 2 x e^sin x

    x e^sin x [ x cos x + 2 ]

  • Calculus grade 12 -

    The answer for b) is e^-4(2x) ?

    And everything after that is for c) right. So the final answer for c) would be xe^sinx(xcosx + 2)

    ?

    Thankyou.

  • Calculus grade 12 -

    In part c) for xcosx could you simplify that or do you keep it as xcosx? Thanks

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