Encontre as Derivadas das Funçōes 1-20 1 f(r)=pi r^2 2 f(x)=3x^2+6x-10 3 f(w)=aw^2+b 4. f(x)=14-(1)/(2)x^-3 5 f(x)=(2x+1)(3x^2+6) 6. f(x)=(7x-1)(x+4) 7 f(x)=(3x^5-1)(2-x^4) 8 f(x)=(2)/(3)(5x-3)^-1(5x+3) 9 f(x)=(x-1)(x+1) 10 f(s)=(s^2-1)(3s-1)(5s^3+2s) 11 f(x)=7(ax^2+bx+c) 12 f(u)=(4u^2-a)(a-2u) 13 f(x)=(2x+4)/(3x-1) 14 f(t)=(t-1)/(t+1) 15 f(t)=(3t^2+5t-1)/(t-1) 16 f(t)=(2-t^2)/(t-2) 17 f(x)=(4-x)/(5-x^2) 18 f(x)=(5x+7)/(2x-2) 19 f(x)=(x+1)/(x+2)(3x^2+6x) 20 f(t)=((t-a)^2)/(t-b)

Vamos corrigir e detalhar as derivadas das funções fornecidas:<br /><br />1. \( f(r) = \pi r^2 \)<br /> \[<br /> f'(r) = 2\pi r<br /> \]<br /><br />2. \( f(x) = 3x^2 + 6x - 10 \)<br /> \[<br /> f'(x) = 6x + 6<br /> \]<br /><br />3. \( f(w) = aw^2 + b \)<br /> \[<br /> f'(w) = 2aw<br /> \]<br /><br />4. \( f(x) = 14 - \frac{1}{2}x^{-3} \)<br /> \[<br /> f'(x) = 0 - \left(-\frac{3}{2}x^{-4}\right) = \frac{3}{2}x^{-4} = \frac{3}{2x^4}<br /> \]<br /><br />5. \( f(x) = (2x + 1)(3x^2 + 6) \)<br /> \[<br /> f'(x) = (2x + 1)(6x) + (3x^2 + 6)(2) = 12x^2 + 6x + 6x^2 + 12 = 18x^2 + 6x + 12<br /> \]<br /><br />6. \( f(x) = (7x - 1)(x + 4) \)<br /> \[<br /> f'(x) = (7x - 1)(1) + (x + 4)(7) = 7x - 1 + 7x + 28 = 14x + 27<br /> \]<br /><br />7. \( f(x) = (3x^5 - 1)(2 - x^4) \)<br /> \[<br /> f'(x) = (3x^5 - 1)(-4x^3) + (2 - x^4)(15x^4) = -12x^8 + 4x^5 + 30x^4 - 15x^8 = -27x^8 + 4x^5 + 30x^4<br /> \]<br /><br />8. \( f(x) = \frac{2}{3}(5x - 3)^{-1}(5x + 3) \)<br /> \[<br /> f'(x) = \frac{2}{3} \left[ (5x - 3)^{-2}(5) + (5x - 3)^{-1}(5) \right] = \frac{2}{3} \left[ \frac{5}{(5x - 3)^2} + \frac{5}{5x - 3} \right] = \frac{2}{3} \left[ \frac{5}{(5x - 3)^2} + \frac{5}{5x - 3} \right]<br /> \]<br /><br />9. \( f(x) = (x - 1)(x + 1) \)<br /> \[<br /> f'(x) = (x + 1)(1) + (x - 1)(1) = x + 1 + x - 1 = 2x<br /> \]<br /><br />10. \( f(s) = (s^2 - 1)(3s - 1)(5s^3 + 2s) \)<br /> \[<br /> f'(s) = (s^2 - 1) \left[ (3s - 1)(5s^2 + 2) + (3s - 1)(10s^2) \right] = (s^2 - 1) \left[ 15s^3 + 6s - 5s^2 - 2 + 30s^3 - 10s^2 \right] = (s^2 - 1) \left[ 45s^3 - 15s^2 + 6s - 2 \right]<br /> \]<br /><br />11. \( f(x) = 7(ax^2 + bx + c) \)<br /> \[<br /> f'(x) = 7(2ax + b)<br /> \]<br /><br />12. \( f(u) = (4u^2 - a)(a - 2u) \)<br /> \[<br /> f'(u) = (4u^2 - a)(-2) + (a - 2u)(8u) = -8u^2 + 2a + 8u^2 - 16u = 2a - 16u<br /> \]<br /><br />13. \( f(x) = \frac{2x + 4}{3x - 1} \)<br /> \[<br /> f'(x) = \frac{(3x - 1)(