Differentiate the following with respect to x(i) y = x-5(ii) y = 5x7/2

1.	Differentiate the following with respect to x(i) y = x-5(ii) y = 5x7/2(iii) y = 8.x5/2x-5/3(iv) y = (2 + x)2(v) y = 3/x5
Answer» (i) dy/dx = -5x^-6 (ii) dy/dx = 5 . 7/2x^{7/2 - 1} = 35/2x^5/2 (iii) y = 8 . x^{(5/2 - 5/3)} = 8x^5/6 (iv) y = (2 + x)² = 4 + 4x + x² dy/dx = d/dx(4 + 4x + x²) = 0 + 4(1) + 2x = 4 + 2x (v) y = 3x^-5 dy/dx = 3(-5x^-6) = - 15x^-6

Differentiate the following with respect to x(i) y = x-5(ii) y = 5x7/2(iii) y = 8.x5/2x-5/3(iv) y = (2 + x)2(v) y = 3/x5

Answer»

(i) dy/dx = -5x^-6

(ii) dy/dx = 5 . 7/2x^{7/2 - 1} = 35/2x^5/2

(iii) y = 8 . x^{(5/2 - 5/3)} = 8x^5/6

(iv) y = (2 + x)² = 4 + 4x + x²

dy/dx = d/dx(4 + 4x + x²)

= 0 + 4(1) + 2x = 4 + 2x

(v) y = 3x^-5

dy/dx = 3(-5x^-6) = - 15x^-6

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