Math, asked by Garrysandhu333, 5 months ago

use chain rule to find the derivative of h(x) =(x+1) (x+2)(x+3).


Answers

Answered by AlluringNightingale
2

Answer :

dh/dx = 3x² + 12x + 11

Note :

If y = u•v , then

dy/dx = v•(du/dx) + u•(dv/dx)

Solution :

  • Given : h(x) = (x + 1)(x + 2)(x + 3)
  • To find : dh/dx = ?

We have ,

h(x) = (x + 1)(x + 2)(x + 3)

Now ,

Differentiating both the sides with respect to x , we have ;

=> dh/dx = d[(x + 1)(x + 2)(x + 3)]/dx

=> dh/dx = d[(x + 1)•(x + 2)(x + 3)]/dx

=> dh/dx = (x + 2)(x + 3)•d(x + 1)/dx

+ (x+1)•d[(x + 2)(x + 3)/dx

=> dh/dx = (x + 2)(x + 3)•1

+ (x+1)•d[(x + 2)•(x + 3)/dx

=> dh/dx = (x + 2)(x + 3) + (x+1)•[(x + 3)•d(x + 2)/dx + (x + 2)•d(x + 3)/dx]

=> dh/dx = (x + 2)(x + 3)

+ (x+1)•[(x + 3)•1 + (x + 2)•1]

=> dh/dx = (x + 2)(x + 3)

+ (x+1)•(x + 3 + x + 2)

=> dh/dx = (x + 2)(x + 3) + (x+1)•(2x + 5)

=> dh/dx = x²+3x+2x+6 + 2x²+ 5x + 2x + 5

=> dh/dx = 3x² + 12x + 11

Hence ,

dh/dx = 3x² + 12x + 11

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