30 PROBLESMAS BASICOS RESUELTOS DE CALCULO DIFERENCIAL

y=-10

y^'=d/dx y=d/dx (-10)=0

y=5

y^'=d/dx y=d/dx (5)=0

f(x)=a^2

f^' (x)=d/dx f(x)=d/dx a^2=0

s(t)=b^2

s^' (t)=d/dt s(t)=d/dx b^2=0

y=6x

y^'=d/dx y=d/dx (6x)=6

y=3/4 x

y^'=d/dx y=d/dx (3/4 x)=3/4

f(x)=ax

f^' (x)=d/dx f(x)=d/dx (ax)=a

s(t)=b^2 t

s^' (t)=d/dt s(t)=d/dx (b^2 t)=b^2

f(x)=5x√2

f^' (x)=d/dx f(x)=d/dx (5x√2)=5√2

y=ax√b

y^'=d/dx y=d/dx (ax√b)=a√b

f(x)=x^5

f^' (x)=d/dx f(x)=d/dx x^5=5x^4

f(x)=4x^3

f^' (x)=d/dx f(x)=d/dx (4x^3 )=4 d/dx x^3=4(3x^2 )=12x^2

s(t)=1/5 t^4

s^' (t)=d/dt s(t)=d/dx (1/5 t^4 )=1/5 d/dx t^4=1/5 (4t^3 )=4/5 t^3

y=x^(9/2)

y^'=d/dx y=d/dx (x^(9/2) )=9/2 x^(9/2-2/2)=9/2 x^(7/2)

f(x)=x^(4/3)

f^' (x)=d/dx f(x)=d/dx x^(4/3)=4/3 x^(4/3-3/3)=4/3 x^(1/3)

y=6x^(3/2)

y^'=d/dx y=d/dx (6x^(3/2) )=6 d/dx x^(3/2)=6(3/2 x^(3/2-2/2) )=9x^(1/2)

f(x)=x^(2/5)

f^' (x)=d/dx f(x)=d/dx x^(2/5)=2/5 x^(2/5-5/5)=2/5 x^(-3/5)

f(x)=4x^(1/4)

f^' (x)=d/dx f(x)=d/dx (4x^(1/4) )=4 d/dx (x^(1/4) )=4(1/4 x^(1/4-4/4) )=x^(-3/4)

f(x)=√x=x^(1/2)

f^' (x)=d/dx f(x)=d/dx x^(1/2)=1/2 x^(1/2-2/2)=1/2 x^(-1/2)

s(t)=∜t=t^(1/4)

s^' (t)=d/dt s(t)=d/dx t^(1/4)=1/4 t^(1/4-4/4)= 1/4 t^(-3/4)

f(x)=5√(5&x)=5x^(1/5)

f^' (x)=d/dx f(x)=d/dx (5x^(1/5) )=5 d/dx (x^(1/5) )=5(1/5 x^(1/5-5/5) )=x^(-4/5)

f(x)=x^5/7

f^'

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