If $y=\frac{\cos x}{1+\sin x}$, then
(a) $\frac{d y}{d x}=\frac{-1}{1+\sin x}$
(b) $\frac{d y}{d x}=\frac{1}{1+\sin x}$
(c) $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$
(d) $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$
If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{t}=\frac{3 \pi}{4}$ is
The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is
If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is
$\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]$ is
If $$y=a \sin x+b \cos x$$, then $$y^2+\left(\frac{d y}{d x}\right)^2$$ is a
If $$f(x)=1+n x+\frac{n(n-1)}{2} x^2+\frac{n(n-1)(n-2)}{6} x^3+\ldots+x^n$$, then $$f^n(1)$$ is equal to :
If $$f(x)$$ and $$g(x)$$ are two functions with $$g(x)=x-\frac{1}{x}$$ and $$f \circ g(x)=x^3-\frac{1}{x^3}$$, then $$f^{\prime}(x)$$ is equals to
If $$y=\left(1+x^2\right) \tan ^{-1} x-x$$, then $$\frac{d y}{d x}$$ is
If $$x=e^\theta \sin \theta, y=e^\theta \cos \theta$$ where $$\theta$$ is a parameter, then $$\frac{d y}{d x}$$ at $$(1,1)$$ is equal to
If $$y=e^{\sqrt{x \sqrt{x} \sqrt{x}}...,} x >1$$, then $$\frac{d^2 y}{d x^2}$$ at $$x=\log _e 3$$ is
If $$f(1)=1, f^{\prime}(l)=3$$, then the derivative of $$f(f(f(x)))+(f(x))^2$$ at $$x=1$$ is
If $$y=x^{\sin x}+(\sin x)^x$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{2}$$ is
If $$e^y+x y=e$$ the ordered pair $$\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)$$ at $$x=0$$ is equal to
If $$a$$ and $$b$$ are fixed non-zero constants, then the derivative of $$\frac{a}{x^4}-\frac{b}{x^2}+\cos x$$ is $$m a+n b-p$$, where
If $$y=\left(\cos x^2\right)^2$$, then $$\frac{d y}{d x}$$ is equal to
For constant $$a, \frac{d}{d x}\left(x^x+x^a+a^x+a^a\right)$$ is
Consider the following statements
Statement 1 : If $$y=\log _{10} x+\log _e x$$, then $$\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}$$
Statement 2 : If $$\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}$$ and $$\frac{d}{d x}\left(\log _e x\right)=\frac{\log x}{\log e}$$
If the parametric equation of curve is given by $$x=\cos \theta+\log \tan \frac{\theta}{2}$$ and $$y=\sin \theta$$, then the points for which $$\frac{d y}{d x}=0$$ are given by
If $$y=(x-1)^2(x-2)^3(x-3)^5$$, then $$\frac{d y}{d x}$$ at $$x=4$$ is equal to
If $$2^x+2^y=2^{x+y}$$, then $$\frac{d y}{d x}$$ is
If $$y=2 x^{n+1}+\frac{3}{x^n}$$, then $$x^2 \frac{d^{2 y}}{d x^2}$$ is
If $$(x e)^y=e^y$$, then $$\frac{d y}{d x}$$ is
If $$[x]$$ represents the greatest integer function and $$f(x)=x-[x]-\cos x$$, then $$f^{\prime}\left(\frac{\pi}{2}\right)=$$
If $$x=a \sec ^2 \theta$$ & $$y=a \tan ^2 \theta$$, then $$\frac{d^2 y}{d x^2}=$$
$$\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}$$, then $$\frac{d y}{d x}=$$