Differentiate the following functions:(i) 1/x (ii) 1/√x (iii) 1/x1/3

1.	Differentiate the following functions:(i) 1/x (ii) 1/√x (iii) 1/x1/3
Answer» We know, d/dx (x^m) = m(x^m-1) (i) d/dx (1/x ) = x^-1 = -x^{– 2} = -1/x² (ii) d/dx (1/√x ) = x^-1/2 = -1/2* x^{– 3/2} (iii) d/dx (1/x^1/3) = x^-1/3 = -1/3 * x^{– 4/3}

Answer»

We know, d/dx (x^m) = m(x^m-1)

(i) d/dx (1/x ) = x^-1 = -x^{– 2} = -1/x²

(ii) d/dx (1/√x ) = x^-1/2 = -1/2* x^{– 3/2}

(iii) d/dx (1/x^1/3) = x^-1/3 = -1/3 * x^{– 4/3}

Discussion

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