Product/Quotient Rules
What is the derivative of f(x)=(x5+4x)(x3-9)
f'(x)=(x5+4x)(3x2)+(x3-9)(5x4+4) or
f'(x)=8x7-45x4+16x3-36
What is the derivative of f(x)=(4x2-8)12
f'(x)=8x(4x2-8)11
What is the derivative of f(x)=sin(x)+cos(x)
f'(x)=cos(x)-sin(x)
What is the line that has a slope of 4 and goes through the point (2,7)
y=4x-1
When does a graph increase and decrease?
Increases when the first derivative is positive, and decreases when the first derivative is negative.
What is the derivative of f(x)=x/x3
f'(x)=-2/x3
What is the derivative of f(x)=4(x4-4)4
f'(x)=64x3(x4-4)3
What is the derivative of f(x)=tan(x)
f'(x)=sec2(x)
What is the line tangent to the function f(x)=2x3 at (1,2)
y=6x-4
When is a graph concave up and concave down?
What is the derivative of f(x)=x3(x-5)4
f'(x)=4x3(x-5)3+3x2(x-5)4
What is the derivative of f(x)=(x2-1)4(x3+3)5
f'(x)=15x3(x2-1)4(x3+3)4+8x(x2-1)3(x3+3)5
What is the derivative of f(x)=sin(x)cos(x)
f'(x)=cos2(x)-sin2(x)
What is the line tangent to the function f(x)=3x3-3x at the point (-2,-18)
y=33x+48
When is a critical point a relative maximum and when is a critical point a relative minimum?
Maximum when the first derivative changes from positive to negative, and a minimum when the first derivative changes from negative to positive.
What is the derivative of f(x)=(x2+2)(x/x2-1)
f'(x)=(x2+2)(-x2-1/(x2-1)2)+2x(x/x2-1)
What is the derivative of f(x)=(2x+4)3/x
f'(x)=(6x2(2x+4)2-(2x+4)3)/x2
What is the derivative of f(x)=csc(4x)
What is the line tangent to f(x)=x3(x2-4) at x=3
y=297x-756
Where are the minimum and maximums of the function f(x)=x/(x2-1)?
Relative maximum at x=-1
Relative minimum at x=1
What is the derivative of f(x)=x/(x1/2-1)
f'(x)=(x1/2-1)-(x/2x1/2)/(x1/2-1)2
What is the derivative of f(x)=(x2/(x-1))3
f'(x)=3(x2-2x)/(x-1)2)(x2/x-1)2
f'(x)=-2xsin(x2)cos(cos(x2))
What is the line tangent to f(x)=x2/(x2+1) at x=-1
y=-1/2x
Where is the function f(x)=x4-6x2 concave up and concave down.
Concave up on the interval (inf,-1)U(1,inf)
Concave down on the interval (-1,1)