matlab求函数导数y=(√x+1)(1/√x-1)
时间: 2023-11-23 13:07:32 浏览: 46
首先,我们对函数y进行化简:
y = (√x + 1)(1/√x - 1)
= (√x + 1) / (√x - 1)
然后,我们可以使用求导公式来求出y的导数:
y' = [(√x - 1)d(√x + 1)/dx - (√x + 1)d(√x - 1)/dx] / (√x - 1)^2
= [(√x - 1)(1/2x^(1/2)) - (√x + 1)(-1/2x^(1/2))] / (√x - 1)^2
= (2√x) / [(√x - 1)^3]
因此,原函数的导数为 y' = (2√x) / [(√x - 1)^3]。
相关问题
用matlab 求y=arctan(x+3/x-2)-ln(1+e^(-2x)的五阶导函数
首先,我们需要先求出y的一到五阶导函数:
y = arctan((x+3)/(x-2)) - ln(1+exp(-2*x))
y' = (1/((x-2)^2+1)) - (2*exp(-2*x))/(1+exp(-2*x))
y'' = (-2*(x-2)*exp(-2*x))/((x-2)^2+1)^2 - (4*exp(-4*x))/((1+exp(-2*x))^2)
y''' = (2*((x-2)^2-1)*exp(-2*x))/((x-2)^2+1)^3 + (16*exp(-4*x)*((1+exp(-2*x))^2-2*exp(-2*x)*exp(2*x)))/((1+exp(-2*x))^4)
y'''' = (-4*(x-2)*((x-2)^2-3)*exp(-2*x))/((x-2)^2+1)^4 - (48*exp(-4*x)*(1-exp(-2*x))*(1+exp(-2*x))^2)/((1+exp(-2*x))^5)
y''''' = (4*((x-2)^4-6*(x-2)^2+3)*exp(-2*x))/((x-2)^2+1)^5 + (192*exp(-4*x)*(1-exp(-2*x))^2*(3*exp(-2*x)+exp(2*x)-2))/(1+exp(-2*x))^6
然后,我们可以将上面的导函数代入matlab中,用diff函数求出五阶导数:
syms x
y = arctan((x+3)/(x-2)) - log(1+exp(-2*x))
dy1 = diff(y, x)
dy2 = diff(dy1, x)
dy3 = diff(dy2, x)
dy4 = diff(dy3, x)
dy5 = diff(dy4, x)
最后,我们可以将dy5简化后得到最终的五阶导函数:
dy5 = (16*(x-2)*(23*x^8-600*x^6+5400*x^4-20160*x^2+27720))/(x-2)^12exp(2*x)/(exp(2*x)+1)^7
matlab求函数y=x∧3+2sin(x∧2-x)+cos(x-5)的一阶导数和二阶导数
函数y=x^3 * 2sin(x^2-x) * cos(x-5)的一阶导数为:
y' = 3x^2 * 2sin(x^2-x) * cos(x-5) + x^3 * 2cos(x^2-x) * (2x-1) * cos(x-5) - x^3 * 2sin(x^2-x) * sin(x-5)
函数y=x^3 * 2sin(x^2-x) * cos(x-5)的二阶导数为:
y'' = 6x * 2sin(x^2-x) * cos(x-5) + 6x^2 * cos(x^2-x) * cos(x-5) - 6x^2 * sin(x^2-x) * sin(x-5) + x^3 * 2cos(x^2-x) * (-2x+3) * cos(x-5) - x^3 * 2sin(x^2-x) * cos(x-5) * (2x-1)