3.4 EXERCISES 1-6 Write the composite function in the form x Identify the inner

Question

3.4 EXERCISES 1-6 Write the composite function in the form x Identify the inner function-gl x) and the outer function y = flu).] Then find the derivative dy/dr. 31, Fr)-' 34. 36 - 38 33. Gix)-4 37, y-cor(ind) -46 Find the derivative of the function. 8· Fix)-(1 + 1 +r)” 10. )- VP-T 11. )-cus(e) 14. ft)sin 16. a) 15. f)esin bi 47-50 Find y and y 47 y-ostsin 30) 49.see 18. glx)- I(x2 48. y tan x) 1-54 Find an equation of the tangent line to the curve at the given 24, Fle}-2' +sia 26. CON 27.l0 55, (a Find an equation of the tangent line to the curve y-2/(1al the point (0, 1) 29. (2) (b) lustrate part (ai hy graphing the caree and the tangent line on the same screea

Explanation / Answer

1) y = (1+4x)1/3
dy/dx = 1/3 ( 1+4x)1/3-1 (4) = 4 (1+4x)-2/3 / 3

2) y = (2x3+5)4
dy/dx = 4(2x3 + 5)4-1 (2*3 x3-1) = 24x2 (2x3+5)3 ;

3) y = tan pi x
dy/dx = sec2 pi x * pi = pi * sec2 pix

4) y = sin (cot x)
dy/dx = cos (cot x) * (- cosec 2 x)
dy/dx = -  cosec2x * cos (cot x)

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