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[let y = f(x)] and to an increment ?x of x, there is a corresponding increase in ?y, then the first derivative

test is

f’(a) = [f (a + h) – f(a)] / h

Where h = ? x and the derivative of f(x) with aspect to x at x = a and denoted by f (a) and f ’(a) is the

derivative if f (a).

i) y = x ^3

ii) y = x + 2

iii) y = 7 / x

i) y = x^3

Differentiating both sides with respect to x, then we get

dy / dx = d / dx (x^3)

dy / dx = 3* x ^ (3 – 1)

dy / dx = 3* x^2

Therefore dy / dx = 3x^2

ii) y = x + 2

dy / dx = d / dx ( x+ 2)

dy / dx = d / dx (x) + d / dx (2)

dy / dx = 1 + 0

Therefore dy / dx = 1

iii) Y = 7 / x

Dy / dx = d / dx ( 7 / x)

Dy / dx = 7 * d / dx ( 1/ x)

Dy / dx = 7 * log x.

Therefore dy / dx = 7 log x