Question

Differentiate the following w.r.t.x. i)2x^5-4x-1/x ii)(x^6)^1/5+1/x^7 iii)(4x^2-9)^1/2​

Answer 1

Answer:

in in a row I love today or not to have been in this video

Answer 2

Explanation:

1. 2x⁵-4x-1/x

dy/dx = 2 d/dx (x⁵) - 4 d/dx (x) - d/dx (1/x)

= 10x⁴ - 4 - d/dx (x^-1)

= 10x⁴ - 4 + 1/x²

2. (x⁶)1/5 + 1/x⁷

dy/dx = d/dx (x^6/5) + d/dx (x^-7)

= 6/5x^1/5 - 7x^-8

3. (4x² - 9)^1/2

let t = (4x² - 9) so that y = t^1/2

dt/dx = 8x

dy/dt = 1/2√t = 1/2√(4x²-9)

dy/dx = dt/dx × dy/dt = 8x × 1/2√(4x²-9) {by chain rule of derivation}

= 4x/√(4x²-9)