What is the Derivative of Functions with Radical and Fractional Exponents?

[disfused_3289]

I'm having trouble with the following questions about differention with respect to x.

Differentiate with respect to x:

a)

y= 2/ (2x+3)^4

b)

y= x(x+1)^(1/2)

c)

y= (x +1)(x^2 + 3x)^3

d)

y= 3x^3 + 3x^(-1/2) + 2



Any help would be greatful

 

[daveb]

Have you learned the chain rule yet?

 

[Hootenanny]

a) y= 2/ (2x+3)^4

Re-write as;

y = 2(2x+3)^{-4}

And use the chain rule.

b)y= x(x+1)^(1/2)
c)y= (x +1)(x^2 + 3x)^3

Chain rule and product rule

d) y = 3x^3 + 3x^(-1/2) + 2

Just use the power rule.

 

[disfused_3289]

Yes, I have learned chain rule

to differentiate from x you find dy/dx

 

[disfused_3289]

Here are my solutions, I don;t know if they're correct

a)

y= 2/ (2x+3)^4

= -4(2x +5)^(-5) x 2 x 2

= -16/ (2x + 5) ^ (-5)

b)

y= x(x+1)^(1/2)

= ( x + 2) (x + 1)^ (1/2) / 2

d)

y = 3x^3 + 3x^(-1/2) + 2

= 3x^2 - 3/2x^(1/3)

 

[Hootenanny]

Here are my solutions, I don;t know if they're correct

a)

y= 2/ (2x+3)^4

= -4(2x +5)^(-5) x 2 x 2

= -16/ (2x + 5) ^ (-5)

Almost, where's the +5 come from in the bracket? And are you sure that should be a -5?

b)
y= x(x+1)^(1/2)
= ( x + 2) (x + 1)^ (1/2) / 2

I'm not sure where your coming from with that, perhaps if you posted your steps?