Question

find the derivative of ( x^3-27) by first principle..

Answer 1

first we write the formula
f'x lin x→0 = f(x+h) - f(x) / h

now f'x = x3 -27

=limh→0[(x+h)3−27]−(x3−27)h=
limh→0[(x+h)3−27]−(x3−27)h
=limh→0x3+h3+3x2h+3xh2−x3h
=limh→0x3+h3+3x2h+3xh2−x3h
=limh→0h3+3x2h+3xh2h
=limh→0h3+3x2h+3xh2h
=limh→0(h2+3x2+3xh)
=limh→0(h2+3x2+3xh)
=0+3x2+0=3x2=0+3x2+0=3x2