Mathematics

# If $y=2^23^{2x}5^{-5}7^{-5}$ then $\dfrac{dy}{dx}=$

##### SOLUTION
$y={ 2 }^{ 2 }{ 3 }^{ 2x }{ 5 }^{ -5 }{ 7 }^{ -7 }\\ y={ 2 }^{ 2 }{ 5 }^{ -5 }{ 7 }^{ -7 }{ 3 }^{ 2x }\\ \dfrac { dy }{ dx } ={ 2 }^{ 2 }{ 5 }^{ -5 }{ 7 }^{ -7 }{ 3 }^{ 2x }\log { 2x } \quad (2)\\ \dfrac { dy }{ dx } ={ 2 }^{ 3 }{ 5 }^{ -5 }{ 7 }^{ -7 }{ 3 }^{ 2x }\log { 2x } \quad$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Hard
Let $I_{1}=\int_{-2}^{2} \dfrac{x^{6}+3 x^{5}+7 x^{4}}{x^{4}+2} d x$ and$I_{2}=\int_{-3}^{1} \dfrac{2(x+1)^{2}+11(x+1)+14}{(x+1)^{4}+2} d x,$ then the value of$I_{1}+I_{2}$ is
• A. 8
• B. $200 / 3$
• C. None of these
• D. $100 / 3$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The solution of $\displaystyle \int_{-\pi }^{\pi }\frac{2x\left ( 1+\sin x \right )}{1+\cos ^{2}x}dx$, is
• A. $\displaystyle \frac{\pi ^{2}}{4}$
• B. $0$
• C. $\displaystyle \frac{\pi }{2}$
• D. $\pi ^{2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate:

$\displaystyle\int_{0}^{\pi/2}\dfrac{\sin\theta}{\sqrt{1+\cos\theta}}d\theta$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Solve $\int {\cos 2x\cos 4xcos6xdx}$.
• A. $I= {\dfrac{1}{4}[\dfrac{\sin12x}{12}+\dfrac{\sin8x}{8}-\dfrac{\sin4x}{4}+x]+c}$
• B. $I= {\dfrac{5}{4}[\dfrac{\sin12x}{12}-\dfrac{\sin8x}{8}+\dfrac{\sin4x}{4}+x]+c}$
• C. None of these
• D. $I= {\dfrac{1}{4}[\dfrac{\sin12x}{12}+\dfrac{\sin8x}{8}+\dfrac{\sin4x}{4}+x]+c}$

$\int \frac{1}{1+x}\;dx$