find the derivative of
6x^6*sqrtx+5/(x^2+sqrtx)
2007-08-26 08:40:04 · 3 answers · asked by Mr. Rain 1 in Science & Mathematics ➔ Mathematics
product rule followed by quotient rule. deriv of sqrt x = deriv x^1/2 = 1/2 x ^ (-1/2) or 1/(2 sqrt x)
2007-08-26 08:58:11 · answer #1 · answered by hayharbr 7 · 1⤊ 0⤋
Use the product rule for the first term and the second is just of the form 1/u
d(uv)/dx = udv/dx + vdu/dx
d(1/u)/dx = (-1/u^2) du/dx
This should be sufficient so you can fill in the details
2007-08-26 15:59:19 · answer #2 · answered by Captain Mephisto 7 · 0⤊ 0⤋
(6x^6*sqrtx)'+(5/(x^2+sqrtx))'
=6x^6*(sqrtx)'+(6x^6)'sqrtx - 5*(x^2+sqrtx)'/(x^2+sqrtx)²
=6x^6*1/(2*sqrtx)+36x^5 sqrtx - 5*(2x+1/2*sqrtx)/(x^2+sqrtx)²
=3x^5,5 + 36x^5,5 - (10x + 2,5/sqrtx)/(x²+sqrtx)²
=39 x^5,5 - (10x + 2,5/sqrt(x))/(x²+sqrt(x))²
2007-08-26 16:08:09 · answer #3 · answered by ?????? 7 · 0⤊ 0⤋