Derivative Question. I am going to retype the equation

Question

anonymous · Answer

$$f(x) = \sqrt[3]{t^2}+2\sqrt{t^3}$$
This is what have for the derivative, however my book says the answer is wrong. 

$$f'(x) = \frac{ 3 }{ 2}\sqrt{t}+\frac{ 4 }{ 3\sqrt{t} }$$

anonymous · Answer

You know it will be easier if you make them into exponents

anonymous · Answer

And then do the power rule

anonymous · Answer

I did

thefurball · Answer

Write them down first and then do the derivative

anonymous · Answer

I typed my answer

anonymous · Answer

I'm also assuming that's suppose to be f(t)

anonymous · Answer

yea

anonymous · Answer

$$f(t) = \sqrt[3]{t^2}+2\sqrt{t^3} \implies f(t) = t^{2/3}+2t^{3/2}$$ right?

welshfella · Answer

convert to exponent form
f(x)  = t^(2/3) + 2t^(3/2)

now use the derivative formula for algebraics

anonymous · Answer

$$t^\frac{ 2 }{ 3 }+2t^\frac{ 3 }{ 2 }$$

anonymous · Answer

$$\huge f'(t) = \frac{ 2 }{ 3 }t^{2/3-1}+\frac{ 3 }{ 2 } \times 2 t^{3/2-1}$$

anonymous · Answer

Ok, i see where i made my mistake

anonymous · Answer

$$\large f'(t) = \frac{ 2 }{ 3 }t^{-1/3}+3t^{1/2} \implies \frac{ 2 }{ 3 } \frac{ 1 }{ \sqrt[3]{t} }+3\sqrt{t}$$