Basic Derivative
Rules
Rules
Find the derivative of this function.
f(x)=3x2+6x+2
f'(x)=6x+6
Find the derivative of this function.
f(x)=(3x+1)2
f'(x)=6(3x+1) OR f'(x)=18x+6
Find the derivative of this function.
f(x)=5sinx-4cosx
f'(x)=5cosx+4sinx
Differentiate this function implicitly.
2x-y=-3
dy/dx=2
Find the derivative of this function.
f(x)=e5x+3
f'(x)=5e5x+3
Find the derivative of this function.
f(x)=2x-10+7x-2
f'(x)=-20x-11-14x-3
Find the derivative of this function.
f(x)=(4x-3)5
f'(x)=20(4x-3)4
Find the derivative of this function.
f(x)=x3sin(5x)
f'(x)=3x2sin(5x)+5x3cos(5x)
Differentiate this function implicitly.
x2+6x-8y+5y2=13
dy/dx=(x+3)/(4-5y)
Find the fourth derivative of this function.
f(x)=3x5+2x3-6x+4
f''''(x)=360x
Find the derivative of this function.
f(x)=(3x-x2)(5+4x)
f'(x)=-24x2+4x+15
Find the derivative of this function.
f(x)=3e4x
f'(x)=12e4x
Find the derivative of this function.
f(x)=cos(x)cot(x)
f'(x)=-csc(x)cot(x)-cos(x)
Differentiate this function implicitly.
xy-y=3
dy/dx=-y/(x-1)
Find the fifth derivative of this function.
f(x)=sin(x)
f(5)(x)=cos(x)
Find the derivative of this function.
f(x)=(x2+1)/x3
f'(x)=(2x3-3x4+3x2)/x6
If f(1)=-5, f(2)=-9, f'(1)=-2, f'(2)=1, g(1)=2, g(2)=4, and g is the inverse of f, find g'(1).
g'(1)=1
Find the derivative of this function.
f(x)=cos(2x)
f'(x)=-2sin(2x)
Differentiate this function implicitly.
x3y3-y=x
dy/dx=1/(3x2y2-1)
Using the limit definition of a derivative, find the derivative, f(x), of the limit below.
lim as h→0 of [3(1+h)2-7(1+h)+1+(3)]/h
f(x)=3x2-7x+1
Find the derivative of this function.
f(x)=(10x+1)/(x2+2)
f'(x)=(-10x2-2x+20)/(x2+2)2
If f(2)=6, f(6)=8, f'(2)=1/3, f'(6)=3/2, and if g is the inverse of f, find g'(6).
g'(6)=3
Find the derivative of this function.
f(x)=-3sin(4x2+5)
f'(x)=-24xcos(4x2+5)
Differentiate this function implicitly.
x3+y3=xy
dy/dx=(y-3x2)/(3y2-x)
Find the derivative of this function.
f(x)=tan-1(x)
f'(x)=1/(1+x2)