y = x^sin⁡x dan y = x^x

Posted by andi telaumbanua on Feb 17, 2018 in Matematika |

Tentukanlah turunan dari :

y = x^sin⁡x dan y = x^x

Jawab:

Use logarithmic derivative

1. ln y = ln x^sin⁡x

ln y = sinx lnx

d/dx (ln⁡ y ) = d/dx(sinx lnx)

d/dy(ln⁡ y) dy/dx = [d/dx (sinx)] (lnx) + sin x [d/dx ( ln⁡x)]

1/y dy/dx = cos⁡ x ln⁡ x + sin⁡x/x

dy/dx = y (cos ⁡x ln⁡ x + sin⁡x/x )

dy/dx = (x^sin⁡x ) (cos⁡ x ln⁡ x + sin⁡x/x )

2. ln y = ln⁡ x^x

ln y = x lnx

d/dx(ln⁡ y) = d/dx(x lnx)

d/dy(ln⁡ y) dy/dx = d/dx(x) (lnx) + x d/dx ( ln⁡ x)

1/y dy/dx = ln⁡ x+ x 1/x

1/y dy/dx = ln⁡ x+1

dy/dx = y (ln x + 1)

dy/dx = x^x (ln x + 1)

for a more clear author please click the link below Tentukanlah turunan dari : 1. y = x^sin⁡x 2. y = x^x

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y = x^sin⁡x dan y = x^x

Tentukanlah turunan dari :

y = x^sin⁡x dan y = x^x

Jawab:

Use logarithmic derivative

1. ln y = ln x^sin⁡x

ln y = sinx lnx

d/dx (ln⁡ y ) = d/dx(sinx lnx)

d/dy(ln⁡ y) dy/dx = [d/dx (sinx)] (lnx) + sin x [d/dx ( ln⁡x)]

1/y dy/dx = cos⁡ x ln⁡ x + sin⁡x/x

dy/dx = y (cos ⁡x ln⁡ x + sin⁡x/x )

dy/dx = (x^sin⁡x ) (cos⁡ x ln⁡ x + sin⁡x/x )

2. ln y = ln⁡ x^x

ln y = x lnx

d/dx(ln⁡ y) = d/dx(x lnx)

d/dy(ln⁡ y) dy/dx = d/dx(x) (lnx) + x d/dx ( ln⁡ x)

1/y dy/dx = ln⁡ x+ x 1/x

1/y dy/dx = ln⁡ x+1

dy/dx = y (ln x + 1)

dy/dx = x^x (ln x + 1)

for a more clear author please click the link below Tentukanlah turunan dari : 1. y = x^sin⁡x 2. y = x^x

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