enEnglishguગુજરાતી
GUJCET · Maths · Continuity and Differentiability
If \(x=\sqrt{10^{\sin ^{-1} t}}, y=\sqrt{10^{\cos ^{-1} t}}\) then, \(\frac{d y}{d x}=\) _________
- A \(0\)
- B \(\frac{y}{x}\)
- C \(-\frac{y}{x}\)
- D \(-\frac{x}{y}\)
Answer & Solution
Correct Answer
(C) \(-\frac{y}{x}\)
Step-by-step Solution
Detailed explanation
\(x^2 = 10^{\sin^{-1} t}, y^2 = 10^{\cos^{-1} t}\) \(x^2 y^2 = 10^{\sin^{-1} t} \cdot 10^{\cos^{-1} t} = 10^{\sin^{-1} t + \cos^{-1} t}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Events A and B are independent events and \(P(A)=P, P(B)=\frac{1}{2}\) and \(P(A \cup B)=\frac{3}{5}\) then, value of \(P\) is _________ .GUJCET 2024 Hard
- \(f\) is continuous at \(x=\frac{\pi}{2}\) where, \(f(x)=\left\{\begin{array}{cc}\frac{2 k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 2024, & x=\frac{\pi}{2}\end{array}\right.\) then, the value of \(k\) is _________GUJCET 2024 Hard
- If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are unit vectors and \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) then, the value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) _________ .GUJCET 2022 Medium
- If \(x=a(1-\cos \theta), y=a(\theta+\sin \theta)\) then, \(\frac{d y}{d x}=\) _________.GUJCET 2024 Medium
- Area of the region bounded by the ellipse \(9 x^2+16 y^2=1\) in the first quadrant is _________ sq. units.GUJCET 2024 Medium
- The angle between the pair of lines \(\vec{r}=-3 \hat{i}+\hat{j}+3 \hat{k}+\lambda(3 \hat{i}+5 \hat{j}+4 \hat{k})\) and \(\vec{r}=-\hat{i}+4 \hat{j}+5 \hat{k}+\mu(\hat{i}+\hat{j}+2 \hat{k})\) is ___________ .GUJCET 2025 Hard
More PYQs from GUJCET
- Multiload 375 is a __________ type of IUDs.GUJCET 2020 Easy
- Type of Hybridisation of N and \(C - N - C\) bond angle in \(\left( CH _3\right)_3 N\) are __________ and __________.GUJCET 2019 Medium
- \(R =\{(1,1),(2,2),(3,3)\}\) is defined on set\(\{x: x \in N, x < 4\}\) then relation \(R =\{(1,1),(2,2),(3,3)\}\) ____________ .GUJCET 2021 Easy
- In which of the following compound all the monosaccharide units are not joined by \(C _1- O - C _4\) chain?GUJCET 2015 Medium
- The number of turns in the coil of an AC generator are 100 and its cross sectional area is \(2.5 m^2\). The coil is revolving in a uniform magnetic field of strength 0.3 T with the uniform angular velocity of \(60 rad s ^{-1}\). The value of maximum induced emf is _________ kV.GUJCET 2017 Hard
- A wire is bent in the form of circle of radius 2 m . Resistance per unit length of wire is \(\frac{1}{\pi} \frac{\Omega}{m}\). Battery of 6 V is connected between A and B. \(\angle \mathrm{AOB}=90^{\circ}\). Find the current through the battery.
GUJCET 2014 Medium