Help me please!! maths test in one day!!?

Question

(e^x)(1+x)^5

please differentiate in respect to x

please full working out and explanations or do not bother at all

thank you very much

Answer 1

You have the chain rule on steriods here:  product rule and exponents.

The product rule means that:

y = A * B (where A and B are expressions that involve an x)

then,

y' = A * B' + A' * B

So for your problem,

y' = (e^x)*[(1+x)^5]' + (e^x)'*(1+x)^5   (notice the two ' marks on the right hand side, which means we need to take derivatives of those items still)

= (e^x)*5(1+x)^4 + (e^x)*(1+x)^5  (the derivative of e^x is e^x)

= (e^x)(1+x)^4(5+(1+x))

= (e^x)(1+x)^4(6+x)

Answer 2

y = (e^x)(1+x)^5

y' = (e^x)' * (1+x)^5 + (e^x) * [(1+x)^5]' = e^x * (1+x)^5 +e^x * 5 * (1+x)^4 * 1 = e^x * (1+x)^4 * (1+x+5) = e^x * (1+x)^4 * (6+x)