Differentiation - Calculus - Mathematics Previous Year Questions

If \(y = {\cos ^2}{{3x} \over 2} - {\sin ^2}{{3x} \over 2}\), then \({{{d^2}y} \over {d{x^2}}}\) is

If \(y = {2^{\log x}}\), then \({{dy} \over {dx}}\) is

If \({x^x} = {y^y}\), then \({{dy} \over {dx}}\) is

The equation of normal to the curve \(y = {(1 + x)^y} + {\sin ^{ - 1}}({\sin ^2}x)\) at \(x = 0\) is

$$\text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }$$

If \(f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}\) then the value of \(f^{\prime}(0)\) is equal to

$$\text { If } x^2+y^2=t+\frac{1}{t} \text { and } x^4+y^4=t^2+\frac{1}{t^2} \text { then } \frac{d y}{d x}=$$

$$\text { If } y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \frac{d y}{d x} \text { equals }$$

$$\text { If } y=f(x), \quad p=\frac{d y}{d x} ; q=\frac{d^2 y}{d x^2} \text { then } \frac{d^2 x}{d y^2} \text { is equal to }$$

$$\text { If } y=\sqrt{\sin x+y} \text { then find } \frac{d y}{d x} \text { at } x=0, \quad y=1$$

$$\text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is }$$

$$\text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to }$$

If \(f(x)=f^{\prime}(x)\) and \(f(1)=2\), then \(f(3)\) is

$$\text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0$$

If $y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$,

then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

The approximate value of \(f(5.001)\), where \(f(x)=x^3-7 x^2+10\)