Question

Tentukan turunan
1. F(x)=e^x-1 Orde 3
2. sin(x)=1/2(e^x-e^-x) orde 4
3. F(x)=sin(2x) orde 4
4. F(x)=ln(1+x) orde 4
5. F(x)=x^3-2x^2+3x+5 orde 3

Answer 1

1.
f(x) = e^x - 1
f'(x) = e^x
f''(x) = e^x
f'''(x) = e^x

2.
f(x) = 1/2 (e^x - e^-x)
f'(x) = 1/2 (e^x - (-e^-x) = 1/2 (e^x + e^x) = 1/2 (2e^x) = e^x
f''(x) = e^x
f'''(x) = e^x
f''''(x) = e^x

3.
f(x) = sin(2x)
f'(x) = 2cos(2x)
f''(x) = -4sin(2x)
f'''(x) = -8cos(2x)
f''''(x) = 16sin(2x)

4.
f(x) = ln(1+x) = ln(x+1)
f'(x) = 1/(x+1)
f''(x) = -1/(x+1)^2
f'''(x) = (2(x+1))/(x+1)^4 = 2/(x+1)^3
f''''(x) = (2.-3(x+1)^2)/(x+1)^6 = -6/(x+1)^4

5.
f(x) = x^3-2x^2+3x+5
f'(x) = 3x^2-4x+3
f''(x) = 6x-4
f'''(x) = 6