Cálculo Derivada de Funciones Compuestas

1. Sea f(x)= (x²-6x+1)^1/2. Calcular la derivada de f(x).

A) f´(x)=(x-3)(x²-6x+1)^1/2
B) f´(x)=(x-3)/(x²-6x+1)^1/2
C) f´(x)=(x-3)/(x²-6x+1)^3/2
D) f´(x)=(x-3)(x²-6x+1)^3/2

2. Sea f(x)= (9x⁵+3x²-8)^1/2. Calcular la derivada de f(x).

A) f´(x)=(45x⁴+6x)(2(9x⁵+3x²-8))^1/2
B) f´(x)=(3/2x)(15x³+6)/(9x⁵+3x²-8)^1/2
C) f´(x)=(45x⁴+6x)/(2(9x⁵+3x²-8))^3/2
D) f´(x)=(3/2x)(15x³+6)/(9x⁵+3x²-8)^5/2

3. Sea f(x)= (x³-5)^6. Calcular la derivada de f(x).

A) f´(x)=x²(x³-5)⁷
B) f´(x)=18x²(x³-5)⁵
C) f´(x)=3x²(x³-5)⁵
D) f´(x)=6x²(x³-5)⁵

4. Sea f(x)= (-4x²-3x+11)^13/7. Calcular la derivada de f(x).

A) f´(x)=(13/7)/(-8x-3)(-4x²-3x+11)^12/7
B) f´(x)=(13/7)(8x+3)/(4x²+3x-11)^6/7
C) f´(x)=-(13/7)(8x+3)(-4x²-3x+11)^6/7
D) f´(x)=(13/7)(-8x-3)(-4x²-3x+11)^12/7

5. Sea f(x)= (1/3x⁸-7x⁵+6x)^1/3. Calcular la derivada de f(x).

A) f´(x)=-(1/3)(24x⁷-35x⁴+6)/(3x⁸-7x⁵+6x)^4/3
B) f´(x)=(24x⁷-35x⁴+6)/(3(3x⁸-7x⁵+6x))^5/3
C) f´(x)=-(24x⁷-35x⁴+6)(3(3x⁸-7x⁵+6x))^2/3
D) f´(x)=(1/3)(24x⁷-35x⁴+6)/(3x⁸-7x⁵+6x)^1/2

6. Sea f(x)=(2x¹¹+8x⁷-15x)^3/5 . Calcular la derivada de f(x).

A) f´(x)=(3/5)(56x⁶-13)/(8x⁷-13x)^2/5
B) f´(x)=(5/3)(56x⁶-13)/(8x⁷-13x)^5/2
C) f´(x)=(3/5)(56x⁶-13)/(8x⁷-13x)
D) f´(x)=(56x⁶-13)/(8x⁷-13x)^2/5

7. Sea f(x)= (x⁵/6+x³/9+x-10)^8. Calcular la derivada de f(x).

A) f´(x)=8(5/6x⁴+1/3x²+1)(1/6x⁵+1/9x³+x-10)⁷
B) f´(x)=(5/6x⁴+1/3x²+1)(1/6x⁵+1/9x³+x-10)⁷
C) f´(x)=(5/6x⁴+1/3x²+1)(1/6x⁵+1/9x³+x-10)⁶
D) f´(x)=8(5/6x⁴+1/3x²+1)(1/6x⁵+1/9x³+x-10)⁶

8. Sea f(x)= sen²(x³) . Calcular la derivada de f(x).

A) f´(x)=6x²sin(x³)cos(x³)
B) f´(x)=3x2sin(x²)cos(x²)
C) f´(x)=3x²sin(2x³)cos(2x³)
D) f´(x)=6x²sin(2x²)cos(2x²)

9. Sea f(x)= Tan(cos(x²)). Calcular la derivada de f(x).

A) f´(x)= - 2xsen(x²)sec²[cos(x²)]
B) f´(x)=- 2sen(x²)sec²[cos(x²)]
C) f´(x)=- 2xsen(2x)sec²[cos(2x)]
D) f´(x)= xsen(x²)sec²[cos(x²)]

10. Sea f(x)= sec(7x³). Calcular la derivada de f(x).

A) f´(x)= 21x²sec(21x²)tan(21x²
B) f´(x)= - x²sec(7x³)tan(7x³
C) f´(x)= - 21sec(21x²)tan(21x²)
D) f´(x)=21x²sec(7x³)tan(7x³)

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