Find the derivative of x=1/2(t^4)-5t-3 using the long method

Question

Find the derivative of x=1/2(t^4)-5t-3 using the long. Show complete solution

Answer 1

Let L = lim h→0

f(t) = t⁴/2 -5t-3

f'(t) = L ((t+h)⁴/2-5(t+h)-3 - t⁴/2+5t+3)/h

= L ((t⁴+4t³h+6t²h²+4th³+h⁴)/2 -5t-5h-3 -t⁴/2+5t+3)/h

= L ((4t³h+6t²h²+4th³+h⁴)/2-5h)/h

= L (4t³+6t²h+4th²+h³)/2 -5

= 4t³/2 - 5

= 2t³-5