Lista resolvida (derivadas)

Função Derivada.

1) Calcule as seguintes derivadas usando a regra da potência, regra de uma soma, de um produto e do quociente: a) f(x) = x5 R: 5x4 b) g(x) = x R: 1 c) h(x) = x10 R: 10x9 d) f(x) = 8x2 R: 16x e) g(z) = -2z7 R: -14z6 f) f(x) = 3x4 + 8x + 15 R: 12x3 + 8 g) g(y) = 9y5 – 4y2 + 2y + 7 R: 45y4 - 8y + 2 h) f(x) = (2x3 – 1)(x4 + x2) R: 14x6 + 10x4 – 4x3 – 2x i) f(t) = 1/2[(t2 + 5)(t6 + 4t)] R: 4t7 + 15t5 + 6t2 + 10 j) f(x) = 2x4 – 3 / x2 – 5x + 3 R: 4x5 – 30x4 + 24x3 + 6x – 15 / (x2 - 5x + 3)2 k) f(x) = 1/x R: -1/x2

2) Calcule as seguintes derivadas: a) f(r) = πr2 R: 2πr b) f(x) = 3x2 + 6x – 10 R: 6x + 6 c) f(w) = aw2 + b R: 2aw d) f(x) = 14 – 1/2x-3 R: 3 / 2x4 e) f(x) = (2x + 1)(3x2 + 6) R: 18x2 + 6x + 12 f) f(x) = (7x – 1)(x + 4) R: 14x + 27 g) f(x) = (3x5 – 1)(2 – x4) R: -27x8 + 30x4 + 4x3 h) f(x) = 2/3(5x – 3)-1(5x + 3) R: -20 / (5x – 3)2 i) f(x) = (x - 1)(x + 1) R: 2x j) f(x) = 7(ax2 + bx + 6) R: 14ax + 7b k) f(x) = (4x2 – a)(a – 2x) R: -24x2 + 8ax + 2a l) f(x) = 2x + 4 / 3x – 1 R: -14 / (3x – 1)2 m) f(t) = t – 1 / t + 1 R: 2 / (t + 1)2 n) f(t) = 3t2 + 5t – 1 / t – 1 R: 3t2 – 6t – 4 / (t – 1)2 o) f(t) = 2 – t2 / t – 2 R: - t2 + 4t – 2 / (t - 2)2 p) f(x) = 4 – x / 5 – x2 R: - x2 + 8x – 5 / (5 – x2)2 q) f(x) = 5x + 7 / 2x – 2 R: - 24 / (2x – 2)2