f'(x) = nx (n - 1)
So,
d/dx(8X)
= 8
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Derivative of sin x = cos x, so chain rule to derive 8x = 8 , answer is 8cos8x
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.
y=(8x).5 + (4x).5 = (2+2sqrt(2))x.5 y'=(1 + sqrt(2))/sqrt(x)
8x + x = 9x
8x + 3 = 50 8x = 47x = 47/8x= 5 and 7/8ths