Derive
f(x) = 3x2
f'(x) = 6x
f(x) = (x3+7x-1)(5x+2)
f'(x) = 20x3+6x2+70x+9
f(x) = (2)/(x+1)
f'(x) = (-2)/(x+1)2
Derive d/x (sinx)
cosx
Define derivative
Instantaneous rate of change of a function
f(x) = 5x3+2x2+5x
f'(x) = 15x2+4x+5
f(x) = x-2(4+3x-3)
f'(x) = - (15+8x3)/(x6)
f(x) = (x2)/(3x-1)
f'(x) = (x(3x-2))/(3x-1)2
Derive d/dx (cosx)
-sinx
Define rate of change
The slope of the tangent line to a function's graph at a point
f(x) = 2x4-10x2+13x
f'(x) = 8x3-20x+13
f(x) = x3lnx
f'(x) = x2(1+3lnx)
f(x) = (3x2)/2-x
f'(x) = (24x-6x2)/(2-x)2
Derive d/dx (tanx)
sec2x
Define differentiable
Has a derivate at a given point; the function is smooth and has a tangent line
f(x) = 6x3-9x+4
f'(x) = 18x2-9
f(x) = 5x2+sinxcosx
f'(x) = 10x+cos2x-sin2x
f(x) = (3x+x4)/(2x2+1)
f'(x) = (4x5+4x3-6x2+3)/(2x2+1)2
d/dx (ex)
ex
Power rule formula
d/dx [x2] = nxn-1
f(x) = 2x3/2-5x-1+x1/3
f'(x) = 3x1/2+5x-2+1/3x-2/3
f(x) = 6x3/2tanx
f'(x) = 3x1/2(2xsec2x+3tanx)
f(x) = (4x3-7x)/(5x2+2)
f'(x) = (20x4+59x2-14)/(5x2+2)2
Derive d/dx (ln(x))
1/x, x>0
Quotient rule formula
f'(x) = (vu' - uv')/v2