Differentiation
Math ⇒ Calculus
Differentiation starts at 11 and continues till grade 12.
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See sample questions for grade 12
Differentiate f(x) = 1/(x2 + 1).
Differentiate f(x) = cos(x).
Differentiate f(x) = ln(3x).
Differentiate f(x) = ln(x) with respect to x.
Differentiate f(x) = x2sin(x).
Find the derivative of f(x) = (x2 + 1)/(x + 1).
Find the derivative of f(x) = 5x3 - 4x + 7.
Find the derivative of f(x) = e2x.
Find the derivative of f(x) = x2ex.
If f(x) = 1/x, what is f′(x)?
The chain rule is used when differentiating which type of functions?
(1) Sums
(2) Products
(3) Compositions
(4) Quotients
Which of the following best describes the meaning of 'differentiable at a point'?
(1) The function is continuous at that point
(2) The function has a derivative at that point
(3) The function is increasing at that point
(4) The function is decreasing at that point
Which of the following is NOT a valid differentiation rule?
(1) Product rule
(2) Quotient rule
(3) Chain rule
(4) Addition rule
Which of the following is the correct derivative of sin(x)?
(1) cos(x)
(2) -cos(x)
(3) -sin(x)
(4) tan(x)
If y = x2 + 3x, then \( \frac{d^2y}{dx^2} \) is _______.
The derivative of tan(x) is _______.
If f(x) = |x|, is f(x) differentiable at x = 0?
True or False: If a function is differentiable at a point, it must also be continuous at that point.
True or False: The derivative of a function at a point gives the slope of the tangent at that point.
True or False: The derivative of ex is ex.
