The product rule states: d/dx uv = vdu/dx + udv/dx
It is not quite clear what your denominator is:
= (1 + x2)-1 d/dx x + x d/dx (1 + x2)-1
= (1 + x2)-1 + x -2x (1 + x2)-2
= (1 + x2)-2 (1 + x2 - 2x2)
= (1 - x2) / (1 + x2)2
= (1 + x)-2 d/dx x + x d/dx (1 + x)-2
= (1 + x)-2 + x -2 (1 + x)-3
= (1 + x)-3 (1 + x - 2x)
= (1 - x)/(1 + x)3
If you prefer, you can use the quotient rule: d/dx (u/v) = (v du/dx - udv/dx) / v2
104
1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 = 1 + 1 + 1 + 1 + 1 + 1 = 5
1 squared (1x1) +3=4
2/x + 1/x2 = (2x+1)/x2
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x
It is -1 over x-squared.
104
∫ (x2+3) = ∫x2 + ∫3(1/3)X3 + 3X + C
The derivative is 1/(1 + cosx)
1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 = 1 + 1 + 1 + 1 + 1 + 1 = 5
arctan(x)
it would be 1 fourth multiplied by quanity d squared plus 3d plus 9 (1/4)(d2 + 3d + 4)
The derivative, with respect to x, is -x/sqrt(1-x2)
1 squared plus 8 squared or 4 squared plus 7 squared
Express as, d/dx[(X)(X2 + 1)1/2 Use the chain rule here after distribution f'(x)g(x) * g'(x) =================================I would leave it at this
x[x+1] squared Simplified is, to my knowledge, x squared plus ( x + 1) squared
The derivative of y = 1/3 x3 - 3x2 + 8x + 1/3 is x2 - 6x + 8. You can determine this for yourself by the rules. The derivative of a constant (e.g. 1/3) is 0. The derivative of xn for positive n (actually all nonzero n) is nxn-1. And if the derivative of f(x) is f'(x), then the derivative of k f(x) is k f'(x). Put all these together and you get the above result.