Question

Help !!!
See question in image.
Please show workings .
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Answer 1

Answer:

Given a function y=f(x) its first derivative – the rate of change of y with respect to x – is defined by: dydx=limh→0[f(x+h)−f(x)h]. Finding the derivative of a function by computing this limit is known as differentiation from first principles

and put the formula answer will be there

Answer 2

Answer:

see explanation

Step-by-step explanation:

Given f(x) then the derivative f'(x) is

f'(x) = lim( h tends to 0 ) $\frac{f(x+h)-f(x)}{h}$

      = lim( h to 0 ) $\frac{\frac{3}{x+h}-\frac{3}{x} }{h}$

     = lim( h to 0 ) $\frac{3x-3(x+h)}{hx(x+h)}$

     = ( lim h to 0 ) $\frac{3x-3x-3h}{hx(x+h)}$

     = lim( h to 0 ) $\frac{-3h}{hx(x+h)}$ ← cancel h on numerator/ denominator

     = lim( h to 0 ) $\frac{-3}{x(x+h)}$ ← let h go to zero, then

f'(x) = - $\frac{3}{x^2}$