F(x+y) = F(x) + F(y) + x^2 *y + x* y^2for all real numbers x and y and ,lim x->0 F(x)/x = 1 求F'(x) = F‘(X) = 1 .作业最后一题了..暗示:F'(x) = lim h->0 F(x+h) - f(x) / h等式就变成 F(x+y) - F(x) = F(y) + x^2y + xy^2
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![F(x+y) = F(x) + F(y) + x^2 *y + x* y^2for all real numbers x and y and ,lim x->0 F(x)/x = 1 求F'(x) = F‘(X) = 1 .作业最后一题了..暗示:F'(x) = lim h->0 F(x+h) - f(x) / h等式就变成 F(x+y) - F(x) = F(y) + x^2y + xy^2](/uploads/image/z/7611941-29-1.jpg?t=F%28x%2By%29+%3D+F%28x%29+%2B+F%28y%29+%2B+x%5E2+%2Ay+%2B+x%2A+y%5E2for+all+real+numbers+x+and+y+and+%2Clim+x-%3E0+F%28x%29%2Fx+%3D+1+%E6%B1%82F%27%28x%29+%3D+F%E2%80%98%EF%BC%88X%EF%BC%89+%3D+1+.%E4%BD%9C%E4%B8%9A%E6%9C%80%E5%90%8E%E4%B8%80%E9%A2%98%E4%BA%86..%E6%9A%97%E7%A4%BA%3AF%27%28x%29+%3D+lim+h-%3E0+F%28x%2Bh%29+-+f%28x%29+%2F+h%E7%AD%89%E5%BC%8F%E5%B0%B1%E5%8F%98%E6%88%90+F%28x%2By%29+-+F%28x%29+%3D+F%28y%29+%2B+x%5E2y+%2B+xy%5E2)
F(x+y) = F(x) + F(y) + x^2 *y + x* y^2for all real numbers x and y and ,lim x->0 F(x)/x = 1 求F'(x) = F‘(X) = 1 .作业最后一题了..暗示:F'(x) = lim h->0 F(x+h) - f(x) / h等式就变成 F(x+y) - F(x) = F(y) + x^2y + xy^2
F(x+y) = F(x) + F(y) + x^2 *y + x* y^2
for all real numbers x and y and ,
lim x->0 F(x)/x = 1
求F'(x) =
F‘(X) = 1 .作业最后一题了..
暗示:F'(x) = lim h->0 F(x+h) - f(x) / h
等式就变成 F(x+y) - F(x) = F(y) + x^2y + xy^2
F(x+y) = F(x) + F(y) + x^2 *y + x* y^2for all real numbers x and y and ,lim x->0 F(x)/x = 1 求F'(x) = F‘(X) = 1 .作业最后一题了..暗示:F'(x) = lim h->0 F(x+h) - f(x) / h等式就变成 F(x+y) - F(x) = F(y) + x^2y + xy^2
应该用导数定义求取:
F'(x)=lim △x->0[F(x+△x)-F(x)]/△x
其中F(x+△x)-F(x)=F(x)+F(△x)+x^2 *△x+x*△x^2-F(x)
=F(△x)+x^2 *△x+x*△x^2;
于是
F'(x)=lim △x->0[F(x+△x)-F(x)]/△x
=lim △x->0[F(△x)+x^2 *△x+x*△x^2]/△x
=x^2+1