Rules for finding derivatives
Solve for derivative using Product and Quotient rules
Solve for derivative using Chain Rule
Properties of Logarithms
Solving Natural Logarithmic equations
100
What is the formula for product rule?
u'v+uv"
100
Use product rule to find the derivative
f(x)=(4x^2)(3x)
f'(x)=36x^2
100
Use the Chain Rule to find the derivative
f(x)=(2x+1)^2
f'(x)=8x+4
100
What is the formula for Product Property?
logb M + logb N=
logb(M*N)
100
Solve natural logarithmic equation
ln(3x+1)=5
Solution
e^ln(3x+1)=e^5
3x+1=148.4
x=49.13
200
What is the formula for chain rule?
g'(u)*u'
200
Use product rule to find the derivative
f(x)=(2x-2)(3x-5)
f'(x)=12x-16
200
Use the Chain Rule to find the derivative
f(x)=(5x+10)^5
f'(x)=25(5x+10)^4
200
What is the formula for Quotient Property?
logb M -logb N=
logb M/logb N
200
Solve natural logarithmic equation
ln(6x-9)=11
Solution
e^ln(6x-9)=e^11
6x-9=59874.1
x=9980.5
300
What is the formula power rule?
300
Use Product rule to find the derivative
f(x)=(x^3-2)(x-5)
f'(x)=4x^3-15x^2-2
300
Use the Chain Rule to find the derivative
f(x)=cos(5x^2-4x+2)
f'(x)=(10x-4)(-sin(5x^2-4x+2)
300
What is the formula for Power Property?
klogb M =
logb M^k
300
Solve natural logarithmic equation
ln(3x)=14
Solution:
e^ln(3x)=e^14
3x=1202604.284
x=400868.0947
400
What is the formula for quotient rule?
u'v-uv'/v^2
400
Use Quotient Rule to find the diravative
f(x)=(2x-2)/(3x-5)
f'(x)=-4/(3x-5)^2
400
Use the Chain Rule to find the derivative
f(x)=sin(3x2+x)
f′(x)=(6x+1)cos(3x2+x)
400
Solve using product property
3log(2x)+log(2y)
Solution:
log(2x)^3+log(2y)
log(8x^3)+log(2y)=
log(16x^3y)
400
Solve natural logarithmic equation
ln(2x-9)=31
Solution
e^ln(2x-9)=e^31
2x-9=2.90x10^13
x=1.45x10^13
500
What are derivatives of trig functions?
500
Use Quotient rule to find the derivative
f(x)=(x^2-4)/(x-3)
f'(x)=x^2-6x+4/(x-3)^2
500
Use the Chain Rule to find the derivative
y=sec(1−5x)
y′=sec(1−5x)tan(1−5x)(−5)
=−5sec(1−5x)tan(1−5x)
500
Solve using quotien property
log(320)-log(34)
Solution
log(320/34)=320/34=9.4
log(9.4)
500
Solve natural logarithmic equation
ln(2x-3)=5
Solution
e^ln(2x-3)=e^5
2x-3=e^5
2x-3=148.4
x=75.7