Basic Derivatives
Product and Quotient Rule
Chain Rule
Implicit Differentiation
Trigonometric Differentiation
Natural Logarithms and Exponentials
tangent lines &
normal lines
normal lines
100
What is the derivative of
y = 3x^2
?
y' = 6x
100
Find the derivative of
y = 3x^2 sin x
3x^2 cos x + 6x sin x
100
Find y' if
y = (3x - 9)^4
12(3x - 9)^3
100
Find the derivative implicitly
x^2 + y^2 = 30
y' = - x/y
100
Find the derivative of
f(x) = 3sinx - 2cosx
3cosx + 2sinx
100
Find the derivative of ln4x^3.
3/x
100
what is the slope of the tangent line? the tangent line is
5x-2.5=-2(y+3)
slope =
-5/2
200
Find the derivative of
f(x) = 5
0
200
Find the derivative of
f(x) = (3x - 2x^2)(5 + 4x)
-24x^2 + 4x + 15
200
Find the derivative of
f(x) = sin 4x
4 cos 4x
200
Find the derivative of sin x + 2cos 2y = 1
y' = cosx/(4sin2y)
200
Find the derivative of y=csc3x^5
y'=-15x^4csc3x^5cot3x^5
200
Find the derivative of y=e^(sinsqrtx)
cossqrtx/(2sqrtx )(e^sinsqrtx)
200
what is the normal line of
f(x)=-1/2x^2+2x+1
y=1(x-3)+2.5
300
Find the derivative of
f(x) = 6x^3 + x - 2
18x2 + 1
300
Find the derivative of
y = (5x - 2)/(x^2 + 1)
(-5x^2 + 4x + 5)/(x^2 + 1)^2
300
Find y' if
y = (9x^2 + 4)^(1/3)
(6x)/(9x^2 + 4)^(2/3
300
Find the derivative of
(y - 2)^2 = 4x - 12
y' = 2/(y - 2)
300
Find the derivative of y=sec5x^5
y'=25x^4sec5x^5tan5x^5
300
Find y'(x).
f(x)=sqrt(5+e^(2x)
e^(2x)/sqrt(5+e^(2x)
300
write the equation for the normal line to
f(x)=(1+x)^(-1/2), x=3
y=16(x-3)+1/2
400
h(x)=f(x)*g(x),
h'(3)= ?
15-8pi
400
Find the derivative of
f(x) = (2x + 5)/(x)^(1/2)
(2x - 5)/(2x^(3/2)
400
f(x) = sin^3 4x
Find f'(x)
12sin^2 4x cos 4x
400
Find dy/dx for
x^3 - 3x^2y + 2xy^2 = 12
y' = (-3x^2 + 6xy - 2y^2)/(-3x^2 + 4xy)
400
Find dy/dx for w(x)=g(x)sinx, w'(0)=?
pi/2
400
w(x)=g(x)sinx,w'(0)=?
w'(0) = π/2
400
Write the equation for the tangent line when (2,1)
Find y' for x^2y+y^2x=6
y'=5/8(x-2)+1
500
Find the third derivative of
5x^5+2x^2+4x
300x^2
500
Find the Derivative of
y= (2x+1)/(2x-1)
y'=-4/(2x-1)^2
500
Find
f'(theta)
f(theta)=secsqrt(theta)
(secsqrt(theta)tansqrt(theta))/(2sqrt(theta))
500
Find dy/dx for x^2y+y^2x=6
y'=(-2xy-y^2)/(x^2+2xy)
500
y=x^3tanx
y' =
=x^3sec^2x+3x^2tanx
500
Find g'(x). g(x)=4xlnx
g'(x) = 4+4lnx
500
If 5x^2+2x^2y+y^2=8
then y' at the point (1,1) is?
y'=-7/2