Derivative Rules
The derivative of f(x)=un
What is f'(x)=nun-1?
The formula for area between the curves for dx
What is the integral of the upper function minus the lower function from the lower x-value bound to the higher x-value bound dx?
What an integral represents on a graph
The derivative of f(x)=x2
What is f'(x)=2x?
The derivative of f(x)=cosx
What is f'(x)=-sinx?
The product rule for f(x)g(x)
What is f'(x)g(x)+f(x)g'(x)?
The formula for area between the curves for dy
What is the integral from the lower y bound to the higher y bound of the right function minus the left function dx?
According to the fundamental theorem of calculus, if a function has an anti-derivative F, then the definite integral of f from a to b is
What is F(b)-F(a)?
The derivative of f(x)=x1/2
What is f'(x)=(1/2)x-1/2?
The derivative of f(x)=tanx
What is f'(x)=sec2x?
The quotient rule of f(x)/g(x)
What is (g(x)f'(x)-f(x)g'(x))/(g(x))2?
The expression for a disk
What is the integral of: (pi)(r2)dx?
Do not forget in a indefinite integral
What is +c!?!?
The derivative of f(x)=(2x+1)/(3x2-1)
What is f'(x)=((3x2-1)(2)-(2x+1)(6x))/(3x2-1)2?
The derivative of f(x)=cscx
What is f'(x)=-cscxcotx?
The derivative of f(x)=lnu
What is f'(x)=(1/u)(du/dx)?
The expression for a washer
What is the integral of: (pi)(R2-r2)dx?
The integral from -1 to 5 of function f(x)=x2-37
What is -180?
f'(3) if f(x)=(3x)(7x2-1)
What is f'(3)=564?
The derivative of f(x)=arccos(u)
What is f'(x)=(-1/(1-u2)1/2)(du/dx)?
The derivative of f(x)=au
What is f'(x)=(aulna)(du/dx)?
The area enclosed between the curves of f(x)=x2 and g(x)=3x2+4x-6 calculated through cross sections of squares perpendicular to the x-axis
What is 136.533?
The integral of (4x)(16-x2)1/2dx
What is (-4(16-x2)3/2)/3 + c?
The derivative of f(x)=(ln2x2)3/e4x
What is f'(x)=((e4x)(3(ln2x2)2(1/(2x2))(4x)-(ln2x2)3(e4x)(4))/(e4x)2?
The derivative of f(x)=arcsec(u)
What is f'(x)=(1/(|u|(u2-1)1/2))(du/dx)?