Calculating Derivatives and Rules

This video tutorial on the Bom Channel covers algebraic derivatives, starting with an introduction and overview. It explains the first derivative using limits, followed by rules and properties of derivatives. Basic exercises are provided to reinforce learning. The video then demonstrates the application of derivative properties in solving problems. Advanced examples using the chain rule are discussed, along with quick methods for special forms. The tutorial concludes with a summary and thanks to viewers.

What is the derivative of a constant function y = c?

• c

• 1

• 0

• c^2

If f(x) = ax^n, what is the general formula for its derivative?

• n * a^(n-1)

• a * x^n

• n * ax^(n-1)

• a * n^x

What is the derivative of a function y = k * u, where k is a constant?

• k * u'

• u

• k

• 0

Which rule is used to find the derivative of a product of two functions?

• Power Rule

• Product Rule

• Quotient Rule

• Chain Rule

What is the derivative of y = u/v using the quotient rule?

• (uv' + u'v)/v^2

• (u'v + uv')/v^2

• (uv' - u'v)/v^2

• (u'v - uv')/v^2

How do you apply the chain rule to find the derivative of a composite function?

• Subtract the derivative of the inner function from the outer function

• Differentiate the outer function and multiply by the derivative of the inner function

• Differentiate the inner function and multiply by the derivative of the outer function

• Add the derivatives of the inner and outer functions

What is the derivative of f(x) = (2x + 3)^5 using the chain rule?

• 10(2x + 3)^5

• 5(2x + 3)^5

• 10(2x + 3)^4

• 5(2x + 3)^4

How is the derivative of a function involving a square root expressed using exponents?

• As a power of 1/2

• As a power of -2

• As a power of -1/2

• As a power of 2

What is the quick method for finding the derivative of a function in the form (ax + b)/(cx + d)?

• (ad - bc)/(cx + d)^2

• (bc - ad)/(cx + d)^2

• (ad + bc)/(cx + d)^2

• (bc + ad)/(cx + d)^2

What is the result of differentiating 2x + 3 with respect to x?

• 2

• 3

• 0

• 5