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differentiate x^3(1+x)^5 with respect for x

First we have to use the product rule, remember that if we have h(x)=f(x)g(x) then h'(x)=f'(x)g(x)+f(x)g'(x).

So h'(x) = x^3D[(x+1)^5]+(x+1)^5D[x^3]

Completing the unfinished derivatives,

h'(x) = x^3[5(x+1)^4]+(x+1)^5[3x^2]

Simplifies to.

h'(x) = 5x^3(x+1)^4+3x^2(x+1)^5

remember that we do the (x+1)^5 in the standard way. 

Robert L. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...

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