10.3 Derivative of Natural Logs
Chapter
Chapter 10
Section
10.3
Solutions 27 Videos

Distinguish between natural logarithms and common logarithms.

0.41mins
Q1

Determine the derivative.

 \displaystyle y = \ln(5x + 8) 

0.28mins
Q3a

Determine the derivative.

 \displaystyle y = \ln(x^2 + 1) 

0.22mins
Q3b

Determine the derivative.

 \displaystyle v = e^t\ln t 

0.59mins
Q3c

Determine the derivative.

 \displaystyle v = \ln \sqrt{x + 1} 

0.37mins
Q3d

Determine the derivative.

 \displaystyle s = \ln (t^3 -2t^2 + 5) 

0.30mins
Q3e

Determine the derivative.

 \displaystyle w = \ln \sqrt{z^2 + 3z} 

1.03mins
Q3f

Differentiate.

 \displaystyle f(x) = x \ln x 

0.17mins
Q4a

Differentiate.

 \displaystyle y = e^{\ln x} 

0.21mins
Q4b

Differentiate.

 \displaystyle y = e^{x} \ln x 

0.27mins
Q4c

Differentiate.

 \displaystyle g(x) = \ln(e^{-x} + x e^{-x}) 

0.43mins
Q4d

Differentiate.

 \displaystyle s = \ln(x^3 - 2x^2 + 5) 

1.06mins
Q4e

Differentiate.

 \displaystyle y = \ln \sqrt{x^2 + 3x} 

1.48mins
Q4f

If g(x) = e^{2x -1}\ln(2x - 1), evaluate g'(1).

1.04mins
Q5a

If f(x) = \ln(\frac{x - 1}{3x + 5}), evaluate f'(5).

0.55mins
Q5b

Solve the equation for f'(x) = 0:

f(x) = \ln(x^2 + 1)

0.28mins
Q6a

Solve the equation for f'(x) = 0: Q6b

Solve the equation for f'(x) = 0:

f(x) = (x^2 + 1)^{-1}\ln(x^2 + 1)

1.04mins
Q6c

Determine the equation of the tangent to the curve defined by f(x) = \frac{\ln \sqrt{x}}{x} at the point where x = 1.

1.30mins
Q7a

Determine the equation of the tangent to the curve defined by y = \ln x - 1 that is parallel to the straight line with equation 3x - 6y - 1 = 0.

1.47mins
Q8

If f(x) = (x\ln x)^2, determine al the points at which the graph of f(x) has a horizontal tangent line.

2.10mins
Q9a

Determine the equation of the tangent to the curve defined by y = \ln(1 + e^{-x}) at the point where x = 0.

1.10mins
Q10

The velocity, in kilometres per hour, of a car as it begins to slow down is given by the equation v(t) = 90- 30\ln(3t + 1), where t is in seconds.

What is the velocity of the car as the driver beings to brake?

0.39mins
Q11a

The velocity, in kilometres per hour, of a car as it begins to slow down is given by the equation v(t) = 90- 30\ln(3t + 1), where t is in seconds.

i. What is the acceleration of the car?

ii. What is the acceleration at t = 2?

0.49mins
Q11bc

The velocity, in kilometres per hour, of a car as it begins to slow down is given by the equation v(t) = 90- 30\ln(3t + 1), where t is in seconds.

How long does the car take to stop?

0.54mins
Q11d

Use the definition of the derivative to evaluate  \displaystyle \lim_{h \to 0} \frac{\ln(2 + h) - \ln 2}{h} 

0.54mins
Q12

Consider f(x) = \ln(\ln x).

a. Determine f'(x).

b. State the domains of f(x) and f'(x).

0.00mins
Q13
Lectures 10 Videos

Introduction to Derivative of ln x with Examples  4.47mins
Introduction to Derivative of ln x with Examples

Derivative of y = a^x   4.14mins
Derivative of a^x   5.13mins
Derivative of log with Examples done in the long way

Derivative of y=\ln|x|

1.42mins
Derivative of ln|x|

## Using Log Laws to Differentiate 3.57mins
Using Log Laws to Differentiate

Derivative of Logarithmic Functions with Chain and Product Rules ex1

2.12mins
Derivative of Logarithmic Functions with Chain and Product Rules ex1

Derivative of Logarithmic Functions with Chain and Product Rules ex2

1.41mins
Derivative of Logarithmic Functions with Chain and Product Rules ex2

Derivative of Logarithmic Functions with Chain and Product Rules ex3

1.41mins
Derivative of Logarithmic Functions with Chain and Product Rules ex3

Derivative of Logarithmic Functions with Chain and Product Rules ex4 