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

Mathematics

2 answers:

Agata [3.3K]3 years ago

8 0

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

koban [17]3 years ago

4 0

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

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