Mastering Differentiation Concepts

What is the derivative of f(x) = x^2?

• 2x

• x^3

• 2x^2

• x

Define the term 'differentiation'.

• Differentiation is the process of finding the derivative of a function.

• Differentiation is the method of solving algebraic equations.

• Differentiation refers to the classification of different types of functions.

• Differentiation is the process of adding two functions together.

What is the power rule in differentiation?

• The power rule applies only to polynomial functions.

• The power rule is used to find the integral of a function.

• The power rule in differentiation is f'(x) = n*x^(n-1) for f(x) = x^n.

• The power rule states f'(x) = n*x^n for f(x) = x^n.

How do you find the derivative of a constant function?

• 1

• The function itself

• A random constant value

• 0

What is the product rule for differentiation?

• (u*v)' = u' + v'

• (u*v)' = u'v' + uv

• (u*v)' = u'v' - uv'

• (u*v)' = u'v + uv'

Explain the quotient rule in your own words.

• The quotient rule states that the derivative of a product of two functions is given by f'(x) = g'(x)h'(x).

• The quotient rule is used to find the integral of a function.

• The quotient rule applies only to polynomial functions.

• The quotient rule states that the derivative of a quotient of two functions is given by f'(x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))^2.

What is the chain rule and when is it used?

• The chain rule applies only to linear functions.

• The chain rule is a method for solving algebraic equations.

• The chain rule is used to integrate functions.

• The chain rule is used to differentiate composite functions.

Find the derivative of f(x) = sin(x).

• cos(x)

• tan(x)

• sin^2(x)

• cosh(x)

What is the derivative of f(x) = e^x?

• e^x

• ln(x)

• x^e

• e^2x

How do you differentiate implicit functions?

• Use the chain rule on y without considering x.

• Differentiate only the y terms in F(x, y) = 0.

• Use implicit differentiation: differentiate both sides of F(x, y) = 0 with respect to x, then solve for dy/dx.

• Set F(x, y) = 1 and solve for y.