Mathematics, 27.02.2020 02:29 4waymari

If f is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = x8f(x) y' = x8f '(x) + 8x7f(x) y' = x8f(x) − 8x7f '(x) y' = x8f(x) + 8x7f '(x) y' = x7f '(x) + 7x8f(x) y' = x7f '(x) − 7x8f(x) (b) y = f(x) x7 y' = xf(x) + 7f '(x) x7 y' = xf '(x) − 6f(x) x8 y' = xf(x) − 7f '(x) x6 y' = xf '(x) + 6f(x) x7 y' = xf '(x) − 7f(x) x8 (c) y = x9 f(x) y' = f '(x)(8x8) − x9f '(x) [f(x)]2 y' = f '(x)(8x9) + x8f(x) [f(x)]2 y' = f(x)(8x9) + x9f '(x) [f(x)]2 y' = f(x)(9x8) − x9f '(x) [f(x)]2 y' = f '(x)(9x8) − x9f(x) [f(x)]2 (d) y = 3 + xf(x) x y' = xf '(x) + 3x2f(x) − 2 2x3/2 y' = xf(x) + 3x2f(x) − 2 2x3/2 y' = xf(x) − 3x2f '(x) + 3 2x3/2 y' = xf(x) + 2x2f '(x) − 3 2x3/2 y' = xf '(x) − 2x2f '(x) + 3 2x3/2

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