Differentiation
Math ⇒ Calculus
Differentiation starts at 11 and continues till grade 12.
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See sample questions for grade 11
Differentiate f(x) = ex with respect to x.
Differentiate y = (3x + 2)4 with respect to x.
Differentiate y = 5x-3 with respect to x.
Differentiate y = ln(2x) with respect to x.
Differentiate y = tan(x) with respect to x.
Differentiate y = x sin(x) with respect to x.
If f(x) = 1/(x + 1), what is f'(x)?
If f(x) = 2x3 and g(x) = x2, find d/dx [f(x)g(x)].
Which of the following is NOT a rule of differentiation?
(1) Product rule
(2) Chain rule
(3) Sum rule
(4) Integral rule
Which of the following is the chain rule for differentiation?
(1) d/dx[f(g(x))] = f'(x)g'(x)
(2) d/dx[f(g(x))] = f'(g(x))g'(x)
(3) d/dx[f(g(x))] = f'(g(x))
(4) d/dx[f(g(x))] = f'(x)g(x)
Which of the following is the correct derivative of y = ax (where a > 0, a ≠ 1)?
(1) ax
(2) ax ln(a)
(3) x ax-1
(4) ln(a)
Which of the following is the derivative of arctan(x)?
(1) 1/(1 + x2)
(2) 1/(1 - x2)
(3) 1/(x2 - 1)
(4) 1/(2x)
The derivative of a function at a point gives the ________ of the tangent to the curve at that point.
The derivative of a function f(x) at x = a is denoted as ________.
The derivative of cos(x) is ________.
The derivative of log10(x) with respect to x is ________.
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 constant is always zero.
True or False: The derivative of a function can be interpreted as the instantaneous rate of change.
True or False: The derivative of a function may not exist at a sharp corner or cusp.
