Basic Diff
Differentiate y=5x^4
y'=20x^3
Differentiate 6x^-2
-12x^-3
Differentiate f(x)=sqrt(x)
f'(x)=1/2x^(-1/2)
Differentiate y=(x+3)^3
y'=3(x+1)^2
Simplify 1-cos^2x
sin^2x
Differentiate y=7x^3-4x
y'=21x^2-4
Differentiate y=5/x^3
y'=-15x^(-4)
Find d/dx(root(3)(x^2))
2/3x^(-1/3)
Find d/dx(2x-5)^4
8(2x−5)^3
Simplify cos^2x/sin^2x
cot^2x
Find d/dx(2x^5+3x-1)
10x^4+3
Find d/dx(4x^2+2/x^2)
8x-4x^-3
Differentiate y=5sqrt(x)+3/sqrt(x)
y'=5/2x^(-1/2)-3/2x^(-3/2)
Differentiate y=sqrt(3x+1)
y'=3/2(3x+1)^(-1/2)
Solve tanx=-1 for 0<x<2pi
x=3/4pi or x=5/4pi
Find the gradient of the normal of y=x^3-3x at x=2 .
-1/9
Find the gradient of the tangent to y=6/x^2 at x=3 .
-4/9
Find the tangent gradient to y=sqrt(x^3) at x=4 .
3
Find the tangent gradient to y=(x^2+1)^3 at x=1 .
24
Simplify cosx+tanxsinx
secx
Find the equation of the tangent of y=x^4-2x^2 at x=1 .
y=-1
For y=10/x , find the angle of inclination of the tangent at x=2 , correct to the nearest degree.
112°
For y=sqrt(x) , find the area of the triangle formed by the tangent at x=1 and the y‑axis.
1.75 unit squared.
Find the equation of the normal to y=(4x-1)^5 at x=0 . Point-gradient form is fine.
y+1=-1/20x
Solve 2cos^2x-cosx-1=0 , where 0<=x<=2pi .
x=0, (2pi)/3, (4pi)/3, or 2pi