Deber de Derivadas.

Universidad de Guayaquil Facultad de Ingeniería Química Carrera de Ingeniería Química
Nombre:	María Fernanda Díaz
Asignatura:	Matemáticas 1
Paralelo:	1er semestre B
Fecha:	25/01/2016
Docente:	Ing. Manuel Fiallos

Deber de  Derivadas
Ejercicios del 9 al 20

Derivadas

Ejercicio 9)

d/dx(3x^4-2x^2+8)

=d/dx(3x^4)-d/dx(2x^2) +d/dx(8)

=3 d/dx(x^4)-2 d/dx(x^2) +d/dx(8)

=3∙4 x^3  d/dx (x)-2∙2 x d/dx(x)

=12x^3-4 x

Ejercicio 10)

d/dx(4+3x-2x^3)

=d/dx(4)+d/dx(3x)-d/dx(2x^3)

=d/dx(4)+3 d/dx(x)-2 d/dx(x^3)

=3 -2∙3 x^2 d/dx(x)

=3-6x^2

Ejercicio 11)

d/dt(at^5-5bt^3)

=d/dt(at^5)-d/dt(5〖bt〗^3)

=a d/dt(t^5)-5b d/dt(t^3)

=a∙5t^4 d/dt(t)-5b∙3t^2 d/dt(t)

=5at^4-15bt^2
 

Ejercicio 12)

d/dz(z^2/2-z^7/7)

=d/dz(z^2/2)-d/dz (z^7/7)

=1/2 d/dz (z^2 )-1/7 d/dz(z^7)

=1/2∙2z d/dz (z)-1/7∙7z^6 d/dz(z)

=2/2 z-7/7 z^6

=z-z^6

Ejercicio 13)

 d/dx √v

=d/dx V^(1⁄2)

=1/2 V^(1⁄2-1) dv/dx

=1/2 v^(-1⁄2) dv/dx

=1/(2√v) dv/dx

Ejercicio 14)

d/dx (2/x-3/x^2)

= d/dx (2/x)-d/dx (3/x^2 )

=2 d/dx (1/x)-3  d/dx (1/x^2 )

=2 d/dx (x^(-1))-3 d/dx(x^(-2))

=2(-1)x^(-1-1) d/dx (x)-3(-2) x^(-2-1 )  d/dx(x)

=-2x^(-2)+6x^(-3)

=-2/x^2 +6/x^(-3) 

Ejercicio 15) 

 d/dt (2t^(4⁄3)-3t^(2⁄3) )

= d/dt (2t^(4⁄3) )-d/dt (3t^(2⁄3))

= 2 d/dt (t^(4⁄3))-3 d/dt (t^(2⁄3))  

= 2(4/3) t^(4⁄3-1) d/dt (t)-3(2/3) t^(2⁄3(-1)) d/dt (t)

=8/3 t^(1⁄3)-2t^(-1⁄3) 

 Ejercicio 16) 

d/dx (2x^(3⁄4)+4x^(-1⁄4))

=d/dx (2x^(3⁄4))+d/dx (4x^(-1⁄4))

=2 d/dx (x^(3⁄4) )+4 d/dx (x^(-1⁄4))

=2(3/4) x^(3⁄4-1) d/dx (x)+4(-1/4) x^(-1⁄4-1) d/dx (x)

=3/2 x^(-1⁄4)-x^(-5⁄4)

 Ejercicio 17)

 d/dx (x^(2⁄3)-a^(2⁄3))

=d/dx (x^(2⁄3))- d/dx (a^(2⁄3))

=2/3 x^(2⁄3-1) d/dx(x)

=2/3 x^(-1⁄3)

Ejercicio 18)

d/dx((a+bx+cx^2)/x)

=d/dx (a/x+bx/x+(cx^2)/x)

=d/dx (a/x+b+cx)

=d/dx (a/x)+d/dx(b)+d/dx(cx)

=a d/dx (1/x)+c d/dx(x)

=a d/dx(x^(-1)) +c

=a(-1) x^(-1-1)  d/dx(x) +c

=-a x^(-2)+c

=c-a/x^2  

Ejercicio 19)

 d/dx (√x/2 -2/√x)

=d/dx (√x/2 )-d/dx (2/√x)

=1/2  d/dx (√x )-2 d/dx (1/√x)

=1/2  d/dx (x^(1⁄2)  )-2 d/dx (x^(-1⁄2) )

=1/2 (1/2) x^(1⁄2-1)  d/dx (x )-2(-1/2) x^(-1⁄2-1)  d/dx (x)

=1/4 x^(-1⁄2)+x^(-3⁄2)

=  1/(4√x)+1/x^(3⁄2) 

=  1/(4√x)+1/√(x^3 )

=  1/(4√x)+1/√(x^2∙x)

=  1/(4√x)+1/(x√x)

Ejercicio 20)

d/dt ((a+bt+ct^2)/√t)

=  d/dt (a/√t+bt/√t+(ct^2)/√t)

= d/dt (t^(-1⁄2) a+t^(-1⁄2) bt +t^(-1⁄2) ct^2)

=  d/dt (at^(-1⁄2)+bt^(1⁄2) +ct^(3⁄2) )

=d/dt (at^(-1⁄2))+d/dt (bt^(1⁄2) )+d/dt (ct^(3⁄2))

= a d/dt (t^(-1⁄2))+b d/dt (t^(1⁄2) )+c d/dt (t^(3⁄2))

=a(-1/2) t^(-1⁄2-1) d/dt (t)+b(1/2) t^(1⁄2-1)  d/dt (t)+c(3/2) t^(3⁄2-1)  d/dt (t)

=-a/2 t^(-3⁄2)+b/2 t^(-1⁄2)+3/2 ct^(1⁄2)

=-a/(2√(t^3 ))+b/(2√t)+(3c√t)/2

=-a/(2√(t^2∙t))+b/(2√t)+(3c√t)/2

=-a/(2t√t)+b/(2√t)+(3c√t)/2