Differentiate each

Question

1. Y= 1/x + 3/x^2 + 2/x^3

2. Y= x^5(1+ x)^5

3. Y= 4-x^2 / 2x+3

Can someone help me I'm lost

Answer 1

1. Just use the power rule
recall that 1/x^2 = x^-2

2. product and chain rule:
y = x^5 (1+x)^5
y' = 5x^4 (1+x)^5 + x^5 * 5(1+x)^4
= 5x^4(1+x)^4 (1+2x)

3. quotient rule. Assuming the usual carelessness with parentheses,

y = (4-x^2)/(2x+3)
y' = [(-2x)(2x+3) - (4-x^2)(2)]/(2x+3)^2
= 2(x^2+3x+4)/(2x+3)^2