MHT CET · Maths · Differentiation
If \(\mathrm{f}(x)=3^x ; \mathrm{g}(x)=4^x\), then \(\frac{\mathrm{f}^{\prime}(0)-\mathrm{g}^{\prime}(0)}{1+\mathrm{f}^{\prime}(0) \mathrm{g}^{\prime}(0)}\) is
- A \(\frac{\log \left(\frac{3}{4}\right)}{1+(\log 3)(\log 4)}\)
- B \(\frac{\log \left(\frac{3}{4}\right)}{1+\log 12}\)
- C \(\frac{\log 12}{1+\log 12}\)
- D \(\frac{\log \left(\frac{3}{4}\right)}{1-\log 12}\)
Answer & Solution
Correct Answer
(A) \(\frac{\log \left(\frac{3}{4}\right)}{1+(\log 3)(\log 4)}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{f}^{\prime}(x)=3^x \log 3 \Rightarrow \mathrm{f}^{\prime}(0)=\log 3 \)
\( \mathrm{~g}^{\prime}(x)=4^x \log 4 \Rightarrow \mathrm{g}^{\prime}(0)=\log 4 \)
\( \therefore \frac{\mathrm{f}^{\prime}(0)-\mathrm{g}^{\prime}(0)}{1+\mathrm{f}^{\prime}(0) \mathrm{g}^{\prime}(0)} =\frac{\log 3-\log 4}{1+(\log 3)(\log 4)} \)
\( =\frac{\log \left(\frac{3}{4}\right)}{1+(\log 3)(\log 4)}\)
\( \mathrm{~g}^{\prime}(x)=4^x \log 4 \Rightarrow \mathrm{g}^{\prime}(0)=\log 4 \)
\( \therefore \frac{\mathrm{f}^{\prime}(0)-\mathrm{g}^{\prime}(0)}{1+\mathrm{f}^{\prime}(0) \mathrm{g}^{\prime}(0)} =\frac{\log 3-\log 4}{1+(\log 3)(\log 4)} \)
\( =\frac{\log \left(\frac{3}{4}\right)}{1+(\log 3)(\log 4)}\)
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
- \(\tan ^{-1} 2+\tan ^{-1} 3=\)MHT CET 2022 Easy
- If the vectors \(\bar{a}=\hat{i}-\hat{j}+2 \hat{k}, \bar{b}=2 \hat{i}+4 \hat{j}+\hat{k}\) and \(\overline{\mathrm{c}}=\mathrm{mi}+\mathrm{j}+\mathrm{nk}\) are mutually perpendicular, then \((\mathrm{m}, \mathrm{n})\) isMHT CET 2024 Easy
- Equation of the plane passing through \((-2,2,2)\) and \((2,-2,-2)\) and perpendicular to the plane \(9 x-13 y-3 z=0\) isMHT CET 2009 Easy
- If and are centroid, orthocenter and circumcenter of a triangle and thenMHT CET 2016 Medium
- The equation of the plane, passing through the mid point of the line segment of join of the points \(\mathrm{P}(1,2,5)\) and \(Q(3,4,3)\) and perpendicular to it, isMHT CET 2024 Easy
- The maximum value of the objective function \(\mathrm{z}=2 \mathrm{x}+3 \mathrm{y}\) subject to the constraints \(\mathrm{x}+\mathrm{y} \leq 5,2 \mathrm{x}+\mathrm{y} \geq 4\) and \(\mathrm{x} \geq 0, \mathrm{y} \geq 0\) isMHT CET 2021 Medium
More PYQs from MHT CET
- A monoatomic gas is suddenly compressed to \((1 / 8)^{\text {th }}\) of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is \((\gamma=5 / 3)\)MHT CET 2021 Easy
- If \(A=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]\),
where \(A_{21}, A_{22}, A_{23}\) are cofactors of \(a_{21}, a_{22}, a_{23}\) respectively, then the value of \(a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}=\)MHT CET 2025 Easy - What is the mass of an fcc unit cell if mass of one atom of an element is \(6 \times 10^{-23} \mathrm{~g}\) ?MHT CET 2020 Easy
- The area (in sq. units) of the region bounded by curves \(y=3 x+1, y=4 x+1\) and \(x=3\) isMHT CET 2023 Medium
- What is the angle between resultant of \(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}\) and \(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}\) ?MHT CET 2020 Easy
- What is the number of carbon atoms in alkanes found in diesel?MHT CET 2020 Easy