Calculus Solver

Practice questions with step-by-step solutions

Tap any question to see its full worked solution. Solutions are saved on this device, so they open instantly next time.

1. Q1.Differentiate $f(x) = x^3 + 2x$.Basic
2. Q2.Find $\dfrac{d}{dx}(\sin x \cos x)$.Basic
3. Q3.Differentiate $y = e^{3x} + \ln x$.Basic
4. Q4.Find $\dfrac{dy}{dx}$ if $y = \dfrac{x^2+1}{x-1}$.Basic
5. Q5.Differentiate $y = \sqrt{1 + x^2}$.Basic
6. Q6.Find $\dfrac{dy}{dx}$ if $y = x^{x}$.JEE Main
7. Q7.If $x^2 + y^2 = 25$, find $\dfrac{dy}{dx}$ at $(3, 4)$.JEE Main
8. Q8.Differentiate $\tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$ with respect to $x$.JEE Main
9. Q9.If $x = a(\theta - \sin\theta)$, $y = a(1 - \cos\theta)$, find $\dfrac{dy}{dx}$.JEE Main
10. Q10.Find the second derivative of $y = e^{x}\sin x$.JEE Main
11. Q11.If $y = (\sin x)^{\cos x} + (\cos x)^{\sin x}$, find $\dfrac{dy}{dx}$.JEE Advanced
12. Q12.If $f(x) = |x-1| + |x-2|$, find where $f$ is not differentiable and find $f'(x)$ elsewhere.JEE Advanced
13. Q13.If $y = \sin^{-1}x$, prove that $(1-x^2)y_2 - x y_1 = 0$.JEE Advanced
14. Q14.Differentiate $\sin(x^2 + 5)$ with respect to $x$.Board Exams
15. Q15.Differentiate $\cos(\sqrt{x})$ with respect to $x$.Board Exams
16. Q16.Find $\dfrac{dy}{dx}$ if $2x + 3y = \sin y$.Board Exams
17. Q17.Find $\dfrac{dy}{dx}$ if $xy + y^2 = \tan x + y$.Board Exams
18. Q18.Differentiate $\sin^{-1}(2x\sqrt{1-x^2})$, $-\tfrac{1}{\sqrt2} < x < \tfrac{1}{\sqrt2}$.Board Exams
19. Q19.Differentiate $\log(\log x)$, $x > 1$.Board Exams
20. Q20.Differentiate $(\log x)^{\cos x}$.Board Exams
21. Q21.If $x = a\cos\theta$, $y = b\sin\theta$, find $\dfrac{dy}{dx}$.Board Exams
22. Q22.If $y = 3\cos(\log x) + 4\sin(\log x)$, show that $x^2y_2 + xy_1 + y = 0$.Board Exams
23. Q23.If $y = e^{a\cos^{-1}x}$, show that $(1-x^2)y_2 - xy_1 - a^2y = 0$.Board Exams
24. Q24.Find the slope of the tangent to $y = x^3 - x$ at $x = 2$.Board Exams
25. Q25.Find the equations of the tangent and normal to $y = x^2 + 4x + 1$ at $x = 3$.Board Exams
26. Q26.Find the intervals in which $f(x) = 2x^3 - 3x^2 - 36x + 7$ is increasing or decreasing.Board Exams
27. Q27.Find the maximum and minimum values of $f(x) = 3x^4 - 8x^3 + 12x^2 - 48x + 25$ on $[0, 3]$.Board Exams
28. Q28.Find the rate of change of the area of a circle with respect to its radius when $r = 5$ cm.Board Exams
29. Q29.Show that of all rectangles with a given perimeter, the square has the maximum area.Board Exams
30. Q30.Check the continuity and differentiability of $f(x) = |x|$ at $x = 0$.Board Exams
31. Q31.Verify Rolle's theorem for $f(x) = x^2 + 2x - 8$ on $[-4, 2]$.Board Exams
32. Q32.Verify the Mean Value Theorem for $f(x) = x^2 - 4x - 3$ on $[1, 4]$.Board Exams
33. Q33.Differentiate $\dfrac{d}{dx}\left(\dfrac{1}{x}\right)$ from first principles.Board Exams
34. Q34.If $f(x) = x^3 + bx^2 + cx + d$ and $0 < b^2 < c$, show that $f$ is strictly increasing on $\mathbb{R}$.JEE Main
35. Q35.Find the point on $y^2 = 4x$ nearest to $(2, 1)$.JEE Main
36. Q36.Let $f(x) = x^3 - 3x + k$. Find all $k$ for which $f(x) = 0$ has three distinct real roots.JEE Advanced