Applying the Chain Rule to Derivatives with Square Roots

[TMNT]

Chain Rule

Question is
Find the derivative of F(x)= 3 sq rt of x^3-1

First step I did was changing the Sq RT to (x^3-1)^3/2
Then I solved it by 3/2(X^3-1)^1/2*3X^2

Another problem very similar
F(X)= 3 SQ RT of X^4+3x+2

Step 1 (X^4+3x+2)^3/2
Then 3/2(X^4+3x+2)*4x^3+3

I know how to do the derivatives my only concern is that 3 in front of the square roots are throwing me off, I just want to know if I'm doing it right.

 

[jth01]

so, your F(x) = 3*sqrt(x^3-1) ?

if so, F'(x) = 3*[1/2(x^3-1)^-1/2]*3x^2 = (9x^2)/(2sqrt(x^3-1))

 

[jth01]

It looks like you're trying to put the coefficient out front into the exponent, like saying 3*(x^1/2) = x^3/2, which it is not. With derivatives that coefficient just kinda stays put...

 

[Rake-MC]

$$3\sqrt{x^3-1} = 3(x^3-1)^{1/2}$$
$$\frac{d}{dx}[3(x^3-1)^{1/2}] = \frac{1}{2} 3 (x^3-1)^{-1/2} 3x^2 = \frac{9x^2}{2\sqrt{x^3-1}}$$

just like jth01 said: $$3x^{1/2}$$ does NOT equal $$x^{3/2}$$

 

[TMNT]

Thanks guys.