Purchase this Material for $10

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
27 Videos

Distinguish between natural logarithms and common logarithms.

Buy to View

Plus Content!
0.41mins

Q1

Determine the derivative.

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

Buy to View

Plus Content!
0.28mins

Q3a

Determine the derivative.

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

Buy to View

Plus Content!
0.22mins

Q3b

Determine the derivative.

```
\displaystyle
v = e^t\ln t
```

Buy to View

Plus Content!
0.59mins

Q3c

Determine the derivative.

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

Buy to View

Plus Content!
0.37mins

Q3d

Determine the derivative.

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

Buy to View

Plus Content!
0.30mins

Q3e

Determine the derivative.

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

Buy to View

Plus Content!
1.03mins

Q3f

Differentiate.

```
\displaystyle
f(x) = x \ln x
```

Buy to View

Plus Content!
0.17mins

Q4a

Differentiate.

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

Buy to View

Plus Content!
0.21mins

Q4b

Differentiate.

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

Buy to View

Plus Content!
0.27mins

Q4c

Differentiate.

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

Buy to View

Plus Content!
0.43mins

Q4d

Differentiate.

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

Buy to View

Plus Content!
1.06mins

Q4e

Differentiate.

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

Buy to View

Plus Content!
1.48mins

Q4f

If `g(x) = e^{2x -1}\ln(2x - 1)`

, evaluate `g'(1)`

.

Buy to View

Plus Content!
1.04mins

Q5a

If `f(x) = \ln(\frac{x - 1}{3x + 5})`

, evaluate `f'(5)`

.

Buy to View

Plus Content!
0.55mins

Q5b

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

:

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

Buy to View

Plus Content!
0.28mins

Q6a

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

:

Buy to View

Plus Content!
Q6b

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

:

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

Buy to View

Plus Content!
1.04mins

Q6c

Determine the equation of the tangent to the curve defined by `f(x) = \frac{\ln \sqrt[3]{x}}{x}`

at the point where x = 1.

Buy to View

Plus Content!
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`

.

Buy to View

Plus Content!
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.

Buy to View

Plus Content!
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`

.

Buy to View

Plus Content!
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?

Buy to View

Plus Content!
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?

Buy to View

Plus Content!
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?

Buy to View

Plus Content!
0.54mins

Q11d

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

Buy to View

Plus Content!
0.54mins

Q12

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

.

a. Determine `f'(x)`

.

b. State the domains of `f(x)`

and `f'(x)`

.

Buy to View

Plus Content!
0.00mins

Q13

Lectures
10 Videos

Introduction to Derivative of ln x with Examples

Buy to View

Plus Content!
4.47mins

Introduction to Derivative of ln x with Examples

Derivative of `y = a^x`

Buy to View

Plus Content!
4.14mins

Derivative of a^x

Derivative of `y=\ln|x|`

Buy to View

Plus Content!
1.42mins

Derivative of ln|x|

Buy to View

Plus Content!
3.57mins

Using Log Laws to Differentiate

Derivative of Logarithmic Functions with Chain and Product Rules ex1

Buy to View

Plus Content!
2.12mins

Derivative of Logarithmic Functions with Chain and Product Rules ex1

Derivative of Logarithmic Functions with Chain and Product Rules ex2

Buy to View

Plus Content!
1.41mins

Derivative of Logarithmic Functions with Chain and Product Rules ex2

Derivative of Logarithmic Functions with Chain and Product Rules ex3

Buy to View

Plus Content!
1.41mins

Derivative of Logarithmic Functions with Chain and Product Rules ex3

Derivative of Logarithmic Functions with Chain and Product Rules ex4

Buy to View

Plus Content!
1.27mins

Derivative of Logarithmic Functions with Chain and Product Rules ex4

Definition of "e"

Buy to View

Plus Content!
5.05mins

Definition of "e"