SOLUTION: i need the derivative of
{{{ x+3*x^(2/3) }}}
i've done it on paper so many times but it doesn't seem to come out right.
there must be some way for the derivative to either
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Question 248504: i need the derivative of
i've done it on paper so many times but it doesn't seem to come out right.
there must be some way for the derivative to either equal 0 or be undefined, and none have my answers have allowed for this. please help!
then i also need the second derivative as well..
Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i need the derivative of
y = x+3*x^(2/3)
--------------------
dy/dx = 1 + 3(2/3)x^(-1/3)
= 1 + 2x^(-1/3)
========================
Cheers,
Stan H.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The derivative of a sum is the sum of the derivatives. So
f'(x) =
I hope you know that the derivative of x is 1. For the derivative of we will use the bring the exponent down in front and subtract 1. This gives us:
f'(x) =
which simplifies to:
f'(x) =
For the second derivative we find the derivative of the first derviative. The derivative of a constant like 1 is zero. And we will repeat the exponent thing on the second term:
f''(x) =
which simplifies to:
f''(x) =
These are the first and second derivatives. You mention something about them being zero. As a general rule derivative are not always zero.
However we are often interested in the value(s) of x that make the derivatives zero. If this is what you are looking for then set the derivatives equal to zero and use Algebra to solve for x. Here's a solution for the x values that make the first derivative zero:
Subtract 1 from each side:
Divide by 2:
Raise each side to the -3 power:
This tells us that the slope of the tangent to f(x) is zero at x = -8.
I will leave it up to you to find the x values, if any, that make the second derivative zero.
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