If $y = a \cos (\log x )$ and $A \frac{d^2 y}{d x^2}+B \frac{d y}{d x}+C=0$, then the values of $A , B , C$ are
- A$x^2,-x,-y$
- ✓$x^2, x, y$
- C$x^2, x_r-y$
- D$x^2,-x, y$
Answer: B.
View full solution →Question types
Differentiation question types
393 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
393
Questions
6
Question groups
5
Question types
01
MCQ
48 Q→02Answer the following questions in short.
34 Q→03Solve the Following Question.(2 Marks)
98 Q→04Solve the Following Question.(3 Marks)
111 Q→05Solve the Following Question.(4 Marks)
54 Q→06Solve the Following Question.(5 Marks)
48 Q→Sample Questions
Differentiation questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If y is a function of x and log(x + y) = 2xy, then the value of y'(0) = _______
- A2
- B-2
- C-1
- ✓1
Answer: D.
View full solution →If $y =\tan ^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right)+\sin \left[2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]$, then $\frac{d y}{d x}=$
- A$\frac{x}{\sqrt{1-x^2}}$
- B$\frac{1-2 x}{\sqrt{1-x^2}}$
- ✓$\frac{1-2 x}{2 \sqrt{1-x^2}}$
- D$\frac{1-2 x^2}{\sqrt{1-x^2}}$
Answer: C.
View full solution →If $y=\sin \left(2 \sin ^{-1} x\right)$, then $\frac{d y}{d x}=$
- ✓$\frac{2-4 x^2}{\sqrt{1-x^2}}$
- B$\frac{2+4 x^2}{\sqrt{1-x^2}}$
- C$\frac{4 x^2-1}{\sqrt{1-x^2}}$
- D$\frac{1-2 x^2}{\sqrt{1-x^2}}$
Answer: A.
View full solution →If $x^y=y^{ x }$, then $\frac{d y}{d x}=$
- A$\frac{x(x \log y-y)}{y(y \log x-x)}$
- ✓$\frac{y(y \log x-x)}{x(x \log y-y)}$
- C$\frac{y^2(1-\log x)}{x^2(1-\log y)}$
- D$\frac{y(1-\log x)}{x(1-\log y)}$
Answer: B.
View full solution →Differentiate the following w. r. t. x.$y=\log \left[\cos \left(x^5\right)\right]$
View full solution →Differentiate the following w. r. t. x.$y=\sqrt{\sin x^3}$
View full solution →Differentiate the following w. r. t. x.$y=\frac{3}{\left(2 x^2-7\right)^5}$
View full solution →Differentiate the following w. r. t. x.$5^{3 \cos x-2}$
View full solution →Differentiate the following w. r. t. x.$\log \left(x^5+4\right)$
View full solution →Differentiate the following w. r. t. x.$y=a^{a^{\log _0(\cos x)}}$
View full solution →Differentiate the following w. r. t. x.$y=(4)^{\log _2(\sin x)}+(9)^{\log _y(\cos x)}$
View full solution →Differentiate the following w. r. t. x.$y=\left(x^3+2 x-3\right)^4(x+\cos x)^3$
View full solution →Differentiate the following w. r. t. x.$y=\cot ^2\left(x^3\right)$
View full solution →Find the $n^{\text {th }}$ derivative of the following : $x^m$
View full solution →If $y=A e^{m x}+B e^{n x}$, show that $y_2-(m+n) y_1+(m n) y=0$.
View full solution →If $y=f(x)$ is a differentiable function of $x$, then show that $\frac{d^2 x}{d y^2}=-\left(\frac{d y}{d x}\right)^{-3} \cdot \frac{d^2 y}{d x^2}$
View full solution →If $x =e^{\frac{x}{y}}$, then show that $\frac{d y}{d x}=\frac{x-y}{x \log x}$
View full solution →If $\sin y=x \sin (a+y)$, then show that $\frac{d y}{d x}=\frac{\sin ^2(a+y)}{\sin a}$
View full solution →Differentiate the following w.r.t. x:
View full solution →$\tan ^{-1}\left[\frac{\sqrt{x}(3-x)}{1-3 x}\right]$
If $y=A \cos (\log x)+B \sin (\log x)$, show that $x^2 y_2+x y_1+y=0$
View full solution →Differentiate the following w.r.t. x:
View full solution →$\tan ^{-1}\left(\frac{x}{1+6 x^2}\right)+\cot ^{-1}\left(\frac{1-10 x^2}{7 x}\right)$
Differentiate the following w.r.t. x:
View full solution →$\cos ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{2}\right)$
Differentiate the following w.r.t. x:
View full solution →$\sin ^2\left[\cot ^{-1}\left(\sqrt{\frac{1+x}{1-x}}\right)\right]$
Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1.
View full solution →
(i) The derivative of f[g(x)] w.r.t. x at x = 0 is _______ (ii) The derivative of g[f(x)] w.r.t. x at x = 0 is _______
(iii) The value of $\left[\frac{d}{d x}\left[x^{10}+f(x)\right]^{-2}\right]_{x=1}$ is
(iv) The derivative of f[(x+g(x))] w.r.t. x at x = 0 is _______
If $x = a \cos \theta, y = b \sin \theta$, show that $a^2\left[y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2\right]+b^2=0$
View full solution →If $\log y=\log (\sin x)-x^2$, show that $\frac{d^2 y}{d x^2}+4 x \frac{d y}{d x}+\left(4 x^2+3\right) y=0$
View full solution →If $y^2=a^2 \cos ^2 x+b^2 \sin ^2 x$, show that $y+\frac{d^2 y}{d x^2}=\frac{a^2 b^2}{y^3}$
View full solution →Differentiate $\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ w.r.t. $\cos ^{-1}\left(\sqrt{\frac{1+\sqrt{1+x^2}}{2 \sqrt{1+x^2}}}\right)$
View full solution →Differentiate $\log \left[\frac{\sqrt{1+x^2}+x}{\sqrt{1+x^2}-x}\right]$ w.r.t. $\cos (\log x)$
View full solution →Generate a Differentiation paper free
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