Differentiability

Definition of Derivative: $f^{'} (x) = lim_{h \to 0} \frac{s i n ( x + h ) - s i n x}{h}$ .
Trigonometric Identity: $sin (x + h) - sin x = 2 cos (x + \frac{h}{2}) sin (\frac{h}{2})$ .
Evaluate Limit: $f^{'} (x) = lim_{h \to 0} \frac{2 c o s ( x + \frac{h}{2} ) s i n ( \frac{h}{2} )}{h} = lim_{h \to 0} cos (x + \frac{h}{2}) \times \frac{s i n ( \frac{h}{2} )}{h /2}$ .
Standard result: $cos (x) \times 1 = cos x$ .

This easy difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of differentiability. It appeared in the 2025 exam.

Looking for more practice? Explore all mathematics questions or browse limit, continuity and differentiability questions on RankGuru.

Differentiability

Select the correct option:

🔒 Solution Hidden from View

More limit, continuity and differentiability Practice Questions

Define f(x) = x^2 for x \le 1 and f(x) = ax + b for x > 1; find a, b making f differentiable everywh...

Consider h(x) = |x - 1| + |x + 1| on the real line; at how many points does h fail to be differentia...

Let p(x) = x^2 \sin(1/x) for x \neq 0 and p(0) = 0; which statement about p at the origin is correct...

If y = x^x for x > 0, then the derivative dy/dx evaluated through logarithmic differentiation equals...

Assertion: every differentiable function is continuous. Reason: differentiability requires the diffe...

Let q(x) = \max{x, x^3} for real x; determine the set of points where q is not differentiable.

Let f(x)=∣x−1∣+∣x−2∣+cos(πx). The number of points where f(x) is non-differentiabl...

The derivative of f(x) = x³ is

If f(x) = eˣ, then f'(x) equals

Using chain rule, d/dx[sin(x²)] equals

About This Question

Solution

Let $f (x) = ∣ x - 1∣ + ∣ x - 2∣ + cos (π x)$ . The number of points where $f (x)$ is non-differentiabl...