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The Chain Rule: Differentiate (x^2 + 1)^5/2 with respect to x

Take one from the power (Un into Un-1) and multiply Un-1 by the old power (n) as well as the differential of the brackets (U')

U=x2 + 1

U'=2x

Un=U5/2      (n=5/2)

Un-1=U3/2

dy/dx= Un-1 * n  * U'

dy/dx= (x2 + 1)3/2  *  5/2  *  2x

dy/dx = 5x(x2 + 1)3/2

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