calculus

find tangent line equation to the curve at the given point:

y= 7e^x cos(x) P=(0,7)

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  1. dy/dx = -7 e^x sin x + 7 e^x cos x

    = 7 e^x (cos x - sin x)

    at (0,7)
    dy/dx = m the slope = 7 e^0 (cos 0 - sin 0)
    = 7
    so y = 7x+b

    at(0,7)
    7 = 7(0) + b
    so b = 7
    and
    y = 7 x + 7
    or
    y = 7(x+1)

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