Differentiation HELP PLEASE!!!!?

Question

1. y = √x

2. y = 6x^2

3. y = x^10+x^20

4. y = x^3+10

5. y = x^3 - 1/x^4

6. y = 2/x√x

7. y = x^2(3x +1)^4

8. y = (2+x^2)/(4-x^4)

9. y = e^x^3

10. y = (e^4x)/(x^2+2)

11. y = ln(x^4+1)^2

12. y = ln(2x/√x+4) [√x + 4 is all under root sign]

Thanks in advance

Answer 1

Remember this,

If y = x^n, y,=nx^(n-1)

1)y = √x

= x^(½)

∴ y, = (½)x^(-½)

=1/2√x

2)y = 6x²

y' = 12x   (use the rule)

3)y = x¹⁰ + x²⁰

y, = 10x⁹ + 20x¹⁹

4)y = x³ + 10

y, = 3x²  (derivative of constant is 0)

5)y = x³ − 1/x⁴

y' = 3x² + 4/x⁵  (remember, 1/x⁴ = x⁻⁴)

6)y = 2/x√x

y, = −3x^(−5/2)

7)y = x²(3x +1)⁴

y, = 4x²(3x +1)³ + 2x(3x +1)⁴  (remember if y = uv, y, = uv, + u,v)

8)y = (2+x²)/(4−x⁴)

y, = [2x(4−x⁴)+4x³(2+x²)]/(4−x⁴)²

9)y = e^x³

y' = 3x²e^x³

10)y = e^4x/(x²+2)

y/ = [4(e^4x)(x²+2) − 2xe^4x]/(x²+2)²

11)y = ln(x⁴+1)²

y, = 8x³/(x⁴+1)

12)y = ln[2x/√(x+4)]

= ln(2x) − ½ln(x+4)

y, = 1/x − 1/2(x+4)

=(x+8)/2(x+4)

Answer 2

3. y = x^10+x^20

y'=10x^9+20x^19

4. y = x^3+10

y' =3x^2

11. y = ln(x^4+1)^2

y' = (2(x^4+1).4x^3 ) /(x^4+1)^2)

do the others