List of top Mathematics Questions on Derivatives asked in JEE Main

Let $( f(x) =$ $\int_0^{x^2 \frac{t^2 - 8t + 15}{e^t} dt}$, $x \in \mathbb{R}$. Then the numbers of local maximum and local minimum points of $ f $, respectively, are:

Let $ f $ be defined as $ R \setminus \{0\} \to R $ such that $ f(x) = \frac{x}{3} + \frac{3}{x} + 3 $ If $ f(x) $ is strictly increasing in $ (-\infty, \alpha_1) \cup (\alpha_2, \infty) $ and strictly decreasing in $ (\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5) $, then $ \sum_{i=1}^5 (\alpha_i)^2 $ is equal to:

If $n-1C_r= (k^2-8)^nC_r+1$ Find $k$.

Let $f(x)$ be a quadratic polynomial with leading coefficient 1 such that $f(0) = p, p≠0$ and $f(1)=\frac{1}{3}$. If the equation $f(x) = 0$ and $fofofof(x) = 0$ have a common real root, then $f(–3)$ is equal to.......................

If $ y(x) = x^x, \, x > 0 $, then $ y''(2) - 2y'(2) $ is equal to:

Let $x(t)=2\sqrt2costsin\sqrt2t $ and $y(t)=2\sqrt2sintsin\sqrt2t$ ,$t ∈(0,\frac{π}{2})$

Then $\frac{1+(\frac{dy}{dx})^2}{\frac{d^2y}{dx^2}}$ at $t=\frac{π}{4}$ is equal to

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Let f and g be twice differentiable even functions on (–2, 2) such that
$ƒ(\frac{1}{4})=0, ƒ(\frac{1}{2})=0, ƒ(1) =1$ and $g(\frac{3}{4}) = 0 , g(1)=2$
.Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

If $\frac{dy}{dx} +2y = sin 2x$ and $y(0) = \frac{3}4$ , then $y (\frac{π}{8})$ is equal to:

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

If y=$\frac{2\cos2\theta+\cos\theta}{\cos3\theta+\cos^2\theta+\cos\theta}$, Then value of y''+y'+y is

If solution of differential equation xdy - ydx = xy(xdy - ydx) and y(1) = 1 is α|y| = |x|e^{(xy - β)} then (α + β) is equal to