Find the derivative of the function 4sqr of x to the 3rd power + 2?

Answer 1

You really ought to use parentheses, even if you don't put your question in equation form. Your function could be interpreted as
1) 4*sqrt(x^3)+2 or
2) 4*sqrt(x)^3+2 or
3) (4*sqrt(x))^3+2,
and the 3rd option is not the same as the other two.
Assuming either 1 or 2, we have 4*x^(3/2)+2. The derivative is
(3/2)*4*x^(3/2 - 1), or 6*x^(1/2).
Assuming option 3 we have (4*x^(1/2))^3+2, or 4^3*x^(3/2)+2. The derivative for this is (3/2)*4^3*x^(3/2 - 1), or 96*x^(1/2).

Answer 2

you really ought to use parentheses, even if you don't put your question in equation form. Your function could be interpreted as
1) 4*sqrt(x^3)+2 or
2) 4*sqrt(x)^3+2 or
3) (4*sqrt(x))^3+2,
and the 3rd option is not the same as the other two.
Assuming either 1 or 2, we have 4*x^(3/2)+2. The derivative is
(3/2)*4*x^(3/2 - 1), or 6*x^(1/2).
Assuming option 3 we have (4*x^(1/2))^3+2, or 4^3*x^(3/2)+2. The derivative for this is (3/2)*4^3*x^(3/2 - 1), or 96*x^(1/2).

Answer 3

I am assuming you mean 4* x^2/3 + 2 ?

Deriv = 2/3 * 4 x^(2/3-1) + 0

= 2/3*4 X^-1/3

=8/3 * x^-1/3