Réponse :
Bonjour
1) f'(t) = (4t + 3)(5t + 3)⁷ + (2t² + 3t)×35(5t + 3)⁶
f'(t) = (5t + 3)⁶[(4t + 3)(5t + 3) + 35(2t² + 3t)]
f'(t) = (5t + 3)⁶(20t² + 27t + 9 + 70t² + 105t)
f'(t) = (5t + 3)⁶(90t² + 132t + 9)
2) f'(t) = [tex]\sqrt{1-2x}[/tex] + (x + 1) * [tex]\frac{-2}{2\sqrt{1-2x} }[/tex]
f'(t) = [tex]\sqrt{1-2x}[/tex] - [tex]\frac{x+1}{\sqrt{1-2x} }[/tex]
f'(t) = [tex]\frac{1-2x-x-1}{\sqrt{1-2x} }[/tex]
f'(t) = [tex]\frac{-3x}{\sqrt{1-2x} }[/tex]
3) f'(t) = 9(3t + 2)²[tex]\sqrt{3t+2}[/tex] + (3t + 2)³ * [tex]\frac{3}{2\sqrt{3t+2} }[/tex]
f'(t) = 3(3t + 2)²(3[tex]\sqrt{3t+2}[/tex] + [tex]\frac{3t+2}{2\sqrt{3t+2} }[/tex] )
f'(t) = 3(3t + 2)² ([tex]\frac{6(3t+2)+3t+2}{2\sqrt{3t+2} }[/tex])
f'(t) = 3(3t + 2)² ([tex]\frac{21t+14}{2\sqrt{3t+2} }[/tex])
4) f'(x) = [tex]\frac{-80(5x+1)^{3} }{16(5x+1)^{8} }[/tex]
f'(x) = [tex]\frac{-5}{(5x+1)^{5} }[/tex]
