How to differentiate y=(x+1)²(x+2)² and y=4x/√2x

Answer 1

y=(x+1)²(x+2)²

Recall the product rule of derivatives,

d/dx(uv)=uv'+vu'

u=(x+1)²

u'=2(x+1)

v=(x+2)²

v'=2(x+2)

dy/dx=(x+1)²*2(x+2)+(x+2)²*2(x+1)

       =2(x+1)(x+2)(x+1+x+2)

        =2(x+1)(x+2)(x+3)

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y=4x/√2x

Recall the product rule of derivatives,

d/dx(u/v)=u'v-v'u/v^2

u=4x

u'=4

v=√2x

v'=√2x^3/2

dy/dx=√2x*4-√2x^3/2*4x/2x

        =4√2x(4-x^2)/2x

Comments

• Derivative of the function y  = (x + 1)²(x + 2)² is 2(x + 1)(x + 2)(2x + 3)

 

• The function
   

Apply The quotient rule in derivatives

Apply derivative on each side with respect of x.

Derivative of the function is .