Differentiating Logarithmic Functions

This video tutorial covers the process of finding derivatives of logarithmic functions, starting with natural logs. It explains the derivative of ln x and extends to more complex functions like ln x squared and ln x cubed. The tutorial also covers derivatives of natural logs involving sums, differences, trigonometric functions, and roots. It further explores derivatives of logarithms with bases other than e and concludes with nested logarithmic derivatives.

What is the derivative of ln(x)?

• 1/x

• x

• x^2

• ln(x)

How can you simplify the derivative of ln(x^2)?

• 2x

• 1/x^2

• x^2

• 2/x

What is the derivative of ln(sin(x))?

• cos(x)

• sin(x)

• cot(x)

• tan(x)

How do you differentiate the natural log of the seventh root of x?

• x^7

• 7/x

• 1/(7x)

• ln(x)/7

What is the formula for the derivative of log base a of u?

• a^u

• ln(a)/u

• u'/u

• u'/(u ln(a))

How do you differentiate log base 4 of x^2?

• 2/(x ln(4))

• x^2 ln(4)

• 2x ln(4)

• 1/(x^2 ln(4))

What is the derivative of log base 7 of (5 - 2x)?

• 5 - 2x

• -2x ln(7)

• 2/(5 - 2x)

• -2/((5 - 2x) ln(7))

How do you find the derivative of log base 5 of tan(x)?

• sec^2(x)/(tan(x) ln(5))

• tan(x) ln(5)

• sec(x) ln(5)

• 1/(tan(x) ln(5))

What is the derivative of the natural log of ln(x)?

• x ln(x)

• ln(x)/x

• 1/x

• 1/(x ln(x))

How do you apply the chain rule to differentiate the cube root of ln(x)?

• 1/(3x (ln(x))^(2/3))

• 3 ln(x)

• ln(x)^(1/3)

• 1/(ln(x)^(1/3))