Use the rules of differentiation to find the derivatives of the following function. Simplify terms wherever possible, but it is not necessary to factorise and then cancel any of the expressions.
2007-08-16 22:27:06 · 2 answers · asked by vanisha j 1 in Science & Mathematics ➔ Mathematics
12x(5x^2-2)^3+180x^3(5x^2-2)^2
(5x^2-2)^2 *(240x^3-24x)
24x(5x^2-2)^2*(10x^2-1)
2007-08-16 22:44:47 · answer #1 · answered by onoris_2020 2 · 0⤊ 0⤋
Use the product rule.
U = 6x^2 and dU/dx = 12x
V = (5x^2-2)^3 and dV/dx = 30x(5x^2 - 2)^2
dF/dx = d(UV)/dx = VdU/dx + UdV/dx
dF/dx = ( (5x^2-2)^3)(12x) + (6x^2)(30x(5x^2 - 2)^2)
dF/dx = ( (5x^2-2)^3)(12x) + (180x^3)((5x^2 - 2)^2)
dF/dx = ((5x^2 - 2)^2)((5x^2-2)12x + 180x^3)
dF/dx = ((5x^2 - 2)^2)(240x^3 - 24x)
dF/dx = 24x((5x^2 - 2)^2)(10x^2 - 1)
Is this good enough?
2007-08-17 05:53:14 · answer #2 · answered by Captain Mephisto 7 · 0⤊ 0⤋