KCET · Maths · Functions
The derivative of \( \cos ^{-1}\left(2 x^{2}-1\right) \) w.r.t \( \cos ^{-1} x \) is
- A \( 12 \)
- B \( -\frac{1}{2 \sqrt{1-x^{2}}} \)
- C \( \frac{2}{x} \)
- D \( 1-x^{2} \)
Answer & Solution
Correct Answer
(A) \( 12 \)
Step-by-step Solution
Detailed explanation
Let \( y=\cos ^{-1}\left(2 x^{2} \quad 1\right)=2 \cos ^{-1} x \) and \( z=\cos ^{-1} x \)
So, \( \frac{d y}{d z}=\frac{d\left(2 \cos ^{-1} x\right)}{d \cos ^{-1} \chi}=2 \)
So, \( \frac{d y}{d z}=\frac{d\left(2 \cos ^{-1} x\right)}{d \cos ^{-1} \chi}=2 \)
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
- In the interval \((0, \pi / 2)\) area lying between the curves \(y=\tan x\) and \(y=\cot x\) and the \(X\)-axis isKCET 2023 Medium
- If \( \vec{a} \) and \( \vec{b} \) are unit vectors then what is the angle between \( \vec{a} \) and \( \vec{b} \) for \( \sqrt{3} \vec{a}-\vec{b} \) to be unit
vector?KCET 2016 Medium - If the eccentricity of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) is \( \frac{5}{4} \) and \( 2 x+3 y-6=0 \) is a focal chord of
the hyperbola, then the length of transverse axis is equal toKCET 2015 Medium - If \(f\left(x^{5}\right)=5 x^{3}\), then \(f^{\prime}(x)\) is equal toKCET 2008 Medium
- \( 3.5 \)
\( \int_{0.2}[x] d x \) is equal toKCET 2017 Hard - The value of
\({ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4\) isKCET 2024 Easy
More PYQs from KCET
- In the following sequence of reactions ;
The compound \( \mathrm{A} \) isKCET 2016 Easy - Area of the region bounded by two parabolas \( y=x^{2} \) and \( x=y^{2} \) isKCET 2014 Hard
- \(A\) and \(B\) are two infinitely long straight parallel conductors. \(C\) is another straight conductor of length \(1 \mathrm{~m}\) kept parallel to \(A\) and \(B\) as shown in the figure. Then the force experienced by \(C\) is
KCET 2007 Hard - The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is \(6 \mu \mathrm{F}\). The value of capacitance of each capacitor isKCET 2020 Easy
- Which of the following is not made by quarks?KCET 2013 Easy
- Which can adsorb larger volume of hydrogen gas?KCET 2022 Easy