List of top Mathematics Questions on Derivatives asked in KEAM

Let \(f(x) = \frac{\sin x}{x}\) for \(x \neq 0\). Then the value of \(f'(\frac{\pi}{2})\) is equal to

If \(y = \sin\left(\tan^{-1}\left(\frac{1}{\sqrt{x^2 - 1}}\right)\right), x > 1\), then \(\frac{dy}{dx} =\)

If \(y = \sqrt{x} + 2\cos(\sqrt{x})\), then the value of \(\frac{dy}{dx}\) at \(x = \frac{\pi^2}{4}\) is equal to

Let $f(x) = \frac{1 + \tan^2 x}{1 - \tan^2 x}$ for $0 < x < \frac{\pi}{4}$. Then the value of $f'(\frac{\pi}{8})$ is equal to

The point $P(x, y)$, where $y = 4\log_e(2)$, lies on the curve with equation $y = \log_e(x^3 + 24)$. Then the value of $\frac{dy}{dx}$ at the point $P$ is

A cubic curve $y = f(x)$ passes through the points $(1, -7)$ and $(2, 11)$. If $\frac{dy}{dx} = 6x^2 + kx - 5$, where $k$ is a constant, then $f(x) =$}

If $f^{\prime}(5)=\frac{3}{5}$ then the value of $\lim_{h\rightarrow 0}\frac{f(5+10h)-f(5)}{h}$ is equal to

If $f(x)=\frac{|x|}{x^{2}}$ then $f^{\prime}(2)$ is equal to

If $f(x)=\tan^{-1}\left(\frac{3\cos x-5\sin x}{5\cos x+3\sin x}\right)$ , then the value $f^{\prime}(1)$ is

If $e^{y}+x^{2}y+xy^{2}=e^{1}$, then $\frac{dy}{dx}$ at (0,1) is equal to ________.

If $f(x)=x|x|$, then $f^{\prime}(-10)=$ ________.

If \( y = \sin^{-1} \left( 2x \sqrt{1 - x^2} \right) \), \( -\frac{1}{\sqrt{2}} \le x \le \frac{1}{\sqrt{2}} \), then \( \frac{dy}{dx} \) is equal to:

If \( y = f(x^2 + 2) \) and \( f'(3) = 5 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:

Let \( f(x) = x^2 + bx + 7 \). If \( f'(5) = 2f'\left(\frac{7}{2}\right) \), then the value of \( b \) is:

If \( y = \sin^{-1} \left( 2x \sqrt{1 - x^2} \right) \), \( -\frac{1}{\sqrt{2}} \le x \le \frac{1}{\sqrt{2}} \), then \( \frac{dy}{dx} \) is equal to:

If \( y = f(x^2 + 2) \) and \( f'(3) = 5 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:

Let \( f(x) = x^2 + bx + 7 \). If \( f'(5) = 2f'\left(\frac{7}{2}\right) \), then the value of \( b \) is:

If \( y = \sin^{-1} \left( 2x \sqrt{1 - x^2} \right) \), \( -\frac{1}{\sqrt{2}} \le x \le \frac{1}{\sqrt{2}} \), then \( \frac{dy}{dx} \) is equal to:

If \( y = f(x^2 + 2) \) and \( f'(3) = 5 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:

Let \( f(x) = x^2 + bx + 7 \). If \( f'(5) = 2f'\left(\frac{7}{2}\right) \), then the value of \( b \) is: