Question

find the derivative of the function f(x)=(3x-2)^{-3/2} + (x ^{2} +1)^{3/2}

Answer 1

So\[f(x)=(3x-2)^{-\frac{ 3 }{ 2 }} + (x ^{2} +1)^{\frac{3}{2}}\]Differentiate this function term by term (act as if it were the sum of two separate functions).
You can use the Power Rule:\[(x^n)' =nx^{n-1}\]Because there are functions between the brackets, you need to appy the Chain Rule as well.
Here, this means multiply the first part with 3 (derivative of 3x-2) and the secont part with 2x (derivative of x²+1).

Answer 2

If you don't succeed, I can help you out!

Answer 3

im lost

Answer 4

OK, first step:\[\left( (3x-2)^{-\frac{3}{2}}\right)'=-\frac{ 3 }{ 2 }(3x-2)^{-\frac{5}{2}} \cdot 3\]See? I used the Power Rule.
The -3/2 is now in front of (3x-2) and the exponent is 1 less, -5/2.
Also I multiplied with 3, because that is the derivative of 3x-2 (Chain Rule).

Now you do the secont one!