प्रथम सिद्धांत से `cos(5x+2)` का अवकल गुणांक ज्ञात कीजिएः

Explanation

माना `y=f(x)=cos (5x+2)`
`Rightarrow f(x+h)=cos [5(x+h)+2]`
`=cos[5x+2+5h]`
ये सभी मान निम्न समीकरण `f'(x)=underset(h to 0)lim (f(x+h)-f(x))/(h)` में रखने पर
`f'(x)=underset(h to 0)lim (cos (5x+2+5h)-cos(5x+2))/(h)`
`=underset(h to 0)lim (1)/(h)[2 sin (5x+2+(5h)/(2))sin((-5h)/(2))]`
`=underset(h to 0)lim (1)/(h)2 sin (5x+2+(5h)/(2)).(sin((5h)/(2)))/(((5h)/(2))).(5h)/(2)`
`=-5sin (5x+2)`