sqrt(X + 13) can be expressed as....
(X + 13)^1/2
so 2/3(X + 13)^3/2
is the antiderivitive
check
multiply coefficient by 3/2 and subtract 1 from exponent
(X + 13)^1/2
sqrt(X + 13)
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the anti-derivative for 2^(1/2) is 2^(1/2)x
The square root of x = x to the power of a half
The derivative of sqrt(2) is zero.
square root of 27 plus the square root of 75
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).