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2) y’ = ln x + x/x = ln x + 1

3) y’ = ln x + 1 – 1 = ln x

4) y’ = 8x⁷e^x + x⁸e^x

5) y’ = 2x3^x + x²3^xln 3

6) y’ = 2x4^x + x²4^xln 4 + 2e^xln x + 2e^x/x

7) y’ = 30^xln 30 ln x + 30^x/x

8) y’ = (xe^x – e^x)/x²

9) y’ = (e^xx² – 2xe^x)/x⁴

10) y’ = (8xe^x – 4x²e^x)/e^2x

11) y’ = (x⁴/x – 4x³ln x)/x⁸ = (1 – 4 ln x)/x⁵

12) y’ = (30e^x/x – 30e^xln x)/25e^2x

13) y’ = 7e^7x

14) y’ = 42e^7x+1

15) y’ = 2(x – 1)(1) = 2x - 2

16) y’ = 12(x² + 4x⁵)¹¹(2x + 20x⁴)

17) y’ = (1/2)(x² + e^x)^-1/2(2x + e^x)

18) y’ = 2(x³ – e^7x)(3x² – 7e^7x)

19) y’ = 4(1/4x) = 1/x

20) y’ = 2x(1/x²) = 2/x

21) y’ = 10x(1/5x²) = 2/x

22) y’ = (1/x²e^x)(2xe^x + x²e^x) = (2 + x)/x

23) y’ = (1/ln 3x)(3*1/3x) = 1/(xln 3x)

24) y’ = e^x(1/e^x) = 1

25) y’ = 2a^2xln a

26) y’ = 2e^{2x + 3}

27) y’ = 5e^5xx² + 2xe^5x

28) y’ = (ln x + x/x)(e^{xln x})

29) y’ = 6(4x³ln x⁴)⁵(12x²ln x⁴ + 16x³/x)

30) Coordinate = (-2, 2)
y’ = 3x² + 6x = 12 – 12 = 0 = slope (y – 2) = 0(x + 2)
y = 2

Answers – Complex Derivatives