Differentiation Grade XI (Science Maha Board)

What does differentiation help us find?

• Total change of a function

• Rate of change of a function at a given point

• Sum of function values

• Maximum value of a function

Which of the following real-life scenarios can be modeled using differentiation?

• Calculating the area of a circle

• Determining the velocity of a moving object

• Finding the sum of a series of numbers

• Measuring the volume of a cube

Why can’t we simply differentiate each term separately in a product of two functions?

• Because each function affects the other’s rate of change

• Because differentiation doesn’t apply to multiplication

• Because the sum rule is easier

• Because differentiation is not needed for products

Why is the Quotient Rule important?

• It simplifies differentiation of trigonometric functions

• It helps differentiate rational functions

• It is the only way to differentiate all functions

• It gives exact values instead of limits

• Sum Rule

• Quotient Rule

• Chain Rule

• Product Rule

Which of the following best explains why differentiation rules (sum, product, quotient) are important?

• They make solving limits easier

• They allow us to find maximum values of functions

• They are used only for trigonometric functions

• They provide structured methods to differentiate complex functions

What is the derivative of f(x) = sin(x) + cos(x)?

• f'(x) = -sin(x) - cos(x)

• f'(x) = -cos(x) + sin(x)

• f'(x) = cos(x) - sin(x)

• f'(x) = sin(x) + sin(x)

• 1