Find the Derivative
Find the first derivative of the following function:
f(x)=(x+1)/(x^3+x-2)
f'(x)=(x^3+x-2-(x+1)(3x^2+1))/(x^3+x-2)^2
Simplified:
(-2x^3-3x^2-3)/(x^3+x-2)^2
Find the critical point(s) of this function:
f(x)=2x^3+3x^2-36x
x=-3 and x=2
Find the global max of this function:
f(x)=3x^2-12x+5 on [0, 3]
Global max: (0, 5)
Find the point(s) of inflection of this function:
f(x)=2x^3+3x^2-36x
x=-1/2
Find the first derivative of the following function:
f(x)=e^(xcosx)
f'(x)=e^(xcosx)(cosx-xsinx)
Find the critical point(s) of this function:
f(x)=x^3+x^2+x
x=-1 and x=1/3
Find the global max of this function:
f(x)=x/(x^2+1) on [0, 2]
Find the point(s) of inflection of this function:
f(x)=x^3+x^2+x
x=-1/3
Find the first derivative of the following function:
f(x)=sin(tanx)
f'(x)=(cos(tanx))/cos^2x
Find the critical point(s) of this function:
f(x)=(x^2)/(x^2+3)
x=0
Find the global min of the following function:
f(x)=x-lnx on [0.5, 2]
Global min: (1, 1)
Find the point(s) of inflection of this function:
f(x)=-2x^2-8x-9
There are no points of inflection.
Find the first derivative of the following function:
x^3+y^3=1
(dy)/(dx)=-(x^2)/(y^2)
Find the critical point(s) of this function:
f(x)=x^(4/5)(x-4)^2
x=0, x=1.143, x=4
Find the global min of the following function:
f(x)=xe^(-x^2/8) on [-1, 4]
Global min: (-1, -0.882)
Find the point(s) of inflection of this function:
f(x)=x^4-x^3-3x^2+4
x=1/2 and x=1
Find the first derivative of the following function:
1+x=sin(xy^2)
dy/dx=(1/cos(xy^2)-y^2)/(xy)
Find the critical point(s) of this function:
f(x)=x^2e^(-3x)
x=0 and x=2/3
Find the global min of the following function:
f(x)=x^4-2x^2-3 on [0, oo)
Find the point(s) of inflection of this function:
f(x)=-3/(16)(x-1)^(4/3)-3/2(x-1)^(1/3)+2
x=1 and x=5