Sample QuestionsDifferentiation (p-1) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $x =\frac{e^t+e^{-t}}{2}, y =\frac{e^t-e^{-t}}{2}$ then $\frac{d y}{d x}=$ ?
- A
$\frac{-y}{x}$
- B
$\frac{y}{x}$
- C
$\frac{-x}{y}$
- ✓
$\frac{x}{y}$
Answer: D.
View full solution →If $x ^4 \cdot y ^5=( x + y )^{( m +1)}$ and $\frac{d y}{d x}=\frac{y}{x}$ then $m =$ ?
Answer: A.
View full solution →If $a x^2+2 hxy + by ^2=0$, then $\frac{d y}{d x}=$ ?
- A
$\frac{(a x+h y)}{(h x+b y)}$
- ✓
$\frac{-(a x+h y)}{(h x+b y)}$
- C
$\frac{(a x-h y)}{(h x+b y)}$
- D
$\frac{(2 a x+h y)}{(h x+3 b y)}$
Answer: B.
View full solution →If $y =\log \left(\frac{e^x}{x^2}\right)$ then $\frac{d y}{d x}=$ ?
- A
$\frac{2-x}{x}$
- ✓
$\frac{x-2}{x}$
- C
$\frac{e-x}{e x}$
- D
$\frac{x-e}{e x}$
Answer: B.
View full solution →If $y =5^{ x } \cdot x ^5$, then $\frac{d y}{d x}=$ ?
- A
$5^x \cdot x^4(5+\log 5)$
- B
$5^x \cdot x^5(5+\log 5)$
- ✓
$5^x \cdot x^4(5+x \log 5)$
- D
$5^x \cdot x^5(5+x \log 5)$
Answer: C.
View full solution →The derivative of $x^m \cdot y^n=(x+y)^{(m+n)}$ is $\frac{x}{y}$
View full solution →The derivative of $a^x$ is $a^x \cdot \log a$.
View full solution →If $y = e ^2$, then $\frac{d y}{d x}=2 e$.
View full solution →If $y =\log x$, then $\frac{d y}{d x}=\frac{1}{x}$
View full solution →$
\frac{d}{d x}\left(10^x\right)=x \cdot 10^{x-1}
$
View full solution →If $x = t . \log t , y = t ^{ t }$ then $\frac{d y}{d x}=\ldots \ldots \ldots \ldots$
View full solution →If $y = e ^{ ax }$, then $x \cdot \frac{d y}{d x}=\ldots \ldots \ldots \ldots$
View full solution →If $x = y +\frac{1}{y}$ then $\frac{d y}{d x}=$
View full solution →If $y =[\log ( x )]^2$ then $\frac{d^2 y}{d x^2}=$
View full solution →If $y = x \cdot \log x$ then $\frac{d^2 y}{d x^2}=$
View full solution →Find $\frac{d^2 y}{d x^2}$, if $y =\log x$
View full solution →Find $\frac{d^2 y}{d x^2}$ if,
$
y=e^{\log x}
$
View full solution →Find $\frac{d^2 y}{d x^2}$ if,
$
y = e ^{(2 x +1)}
$
View full solution →Find $\frac{d^2 y}{d x^2}$ if,
$
y = e ^{ x }
$
View full solution →Find $\frac{d^2 y}{d x^2}$ if,
$
y=x^{-7}
$
View full solution →Find $\frac{d y}{d x}$ if $y = x ^{ x }$.
View full solution →Find the rate of change of demand $(x)$ of a commodity with respect to its price $( y )$ if $y =25+30 x - x ^2$.
View full solution →If $y=[\log (\log (\log x))]^2$, find $\frac{d y}{d x}$
View full solution →Find $\frac{d^2 y}{d x^2}$, if $y = x ^2 \cdot e ^{ x }$
View full solution →Find $\frac{d^2 y}{d x^2}$, if $y =2 at , x = at t ^2$.
View full solution →Find the rate of change of demand $( x )$ of a commodity with respect to its price $( y )$ if $y =\frac{5 x+7}{2 x-13}$
View full solution →If $y =\sqrt[5]{\left(3 x^2+8 x+5\right)^4}$, find $\frac{d y}{d x}$
View full solution →If $y = x ^3+3 x y^2+3 x ^2 y$, find $\frac{d y}{d x}$
View full solution →If $y=\left(6 x^3-3 x^2-9 x\right)^{10}$, find $\frac{d y}{d x}$
View full solution →Find $\frac{d y}{d x}$ if, :
$
x=\sqrt{1+u^2}, y=\log \left(1+u^2\right)
$
View full solution →Find $\frac{d y}{d x}$ if $y =2^{x^x}$.
View full solution →If $x ^{ a } \cdot y ^{ b }=( x + y )^{ a + b }$, then show that $\frac{d y}{d x}=\frac{y}{x}$.
View full solution →Solve the following : If $x = t \cdot \log t , y = t ^{ t }$, then show that $\frac{d y}{d x}- y =0$.
View full solution →Solve the following : If $x =\frac{4 t}{1+t^2}, y =3\left(\frac{1-t^2}{1+t^2}\right)$, then show that $\frac{d y}{d x}=-\frac{9 x}{4 y}$
View full solution →Find $\frac{d y}{d x}$ if, :
$
x =\left(u+\frac{1}{u}\right)^2, y =(2)^{\left(u+\frac{1}{u}\right)}
$
View full solution →Find $\frac{d y}{d x}$ if $y = x ^{ x }+(7 x -1)^{ x }$
View full solution →Find $\frac{d y}{d x}$, if $y =\sqrt{\frac{(3 x-4)^3}{(x+1)^4(x+2)}}$
View full solution →If $a x^2+2 h x y+b y^2=0$, then show that $\frac{d^2 y}{d x^2}=0$.
View full solution →If $x^2+6 x y+y^2=10$, then show that $\frac{d^2 y}{d x^2}=\frac{80}{(3 x+y)^3}$.
View full solution →If $x ^7 \cdot y ^9=( x + y )^{16}$, then show that $\frac{d y}{d x}=\frac{y}{x}$.
View full solution →