I assume you mean -10x^4?
In that case, antiderivative would be to add one to the exponent, then divide by the exponent. So -10x^5, then divide by 5. So the antiderivative is -2x^5.
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By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2
(that weird integral or antiderivative sign) x^(-6/5) dx =-5*x^(-1/5)
10x4^5
It is an inverse function of a derivative, also known as an integral.
The general formula for powers doesn't work in this case, because there will be a zero in the denominator. The antiderivative of 1/x is ln(x), that is, the natural logarithm of x.