f'(x)=.5x^-.5
f''(x)=-.25x^-1.5
f'''(x)=.375x^-2.5 or f'''(x)=(3/8)x^(-5/2)
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It is x to the sixth power.
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Derivative with respect to 'x' of (5x)1/2 = (1/2) (5x)-1/2 (5) = 2.5/sqrt(5x)
Derivative of lnx= (1/x)*(derivative of x) example: Find derivative of ln2x d(ln2x)/dx = (1/2x)*d(2x)/dx = (1/2x)*2===>1/x When the problem is like ln2x^2 or ln-square root of x...., the answer won't come out in form of 1/x.
No. The Square root of x is not the value of x. So it can not be simplified beyond: Root X + root 3x Yes. The square root of 3x equals the square root of 3 times the square root of x, so when you add another square root of x, you can factor out the square root of x, thereby simplifying the expression to the square root of x times the sum of one plus the square root of three.