SOLUTION: not sure if I have the right area
consider the following
6x^3/5+5square root symbol x inside-6/3square root symbol x inside
use the power rule for differentiation to find f'(x).
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Question 200331: not sure if I have the right area
consider the following
6x^3/5+5square root symbol x inside-6/3square root symbol x inside
use the power rule for differentiation to find f'(x). Give your answer using the form below where B>D>F
f'(x)=Ax^B+Cx^D+Ex^F
can someone help please
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There isn't a 'right' area to put this one. This is an elementary calculus problem.
 = 6x^{\frac{3}{5}} + 5\sqrt{x} - \frac{6}{3\sqrt{x}})
Change the radicals to fractional exponents:
 = 6x^{\frac{3}{5}} + 5x^{\frac{1}{2}} - \frac{6}{3x^{\frac{1}{2}}})
Simplify the third term by removing the common factor of 3 from numerator and denominator and moving the variable to the numerator:
 = 6x^{\frac{3}{5}} + 5x^{\frac{1}{2}} - 2x^{-\frac{1}{2}})
Now, since the derivative of the sum is the sum of the derivatives, you can apply the Power Rule to each of the terms separately.
The Power Rule:
 = ax^n \ \ \Rightarrow\ \ f'(x) = nax^{n-1})
So:
 = \frac{18}{5}x^{-\frac{2}{5}} + \frac{5}{2}x^{-\frac{1}{2}} - x^{-\frac{3}{2}})
Which is already the proper order of terms because 
John
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