0

Guest

Courses New

find dy/dx when y= e^(ax) . sec x . log x/ sqrt(1 – 2x)

find dy/dx when
y= e^(ax) . sec x . log x/ sqrt(1 – 2x)

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
\\ \\ \frac{d}{dx}\left(e^{ax}\sec \left(x\right)\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)\right) \\ =\frac{d}{dx}\left(e^{ax}\right)\sec \left(x\right)\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)+\frac{d}{dx}\left(\sec \left(x\right)\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)\right)e^{ax} \\ \frac{d}{dx}\left(\sec \left(x\right)\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)\right) \\ =\frac{d}{dx}\left(\sec \left(x\right)\right)\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)+\frac{d}{dx}\left(\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)\right)\sec \left(x\right) \\ =\frac{\tan \left(x\right)}{\cos \left(x\right)}\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)+\frac{1}{2x\ln \left(10\right)+\frac{\ln \left(10\right)}{x-1}+\ln \left(10\right)}\sec \left(x\right)
\\ =e^{ax}a\sec \left(x\right)\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)+\left(\frac{\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)\tan \left(x\right)}{\cos \left(x\right)}+\frac{\sec \left(x\right)}{2x\ln \left(10\right)+\frac{\ln \left(10\right)}{x-1}+\ln \left(10\right)}\right)e^{ax} \\ =e^{ax}\left(\sec \left(x\right)\left(a\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)+\frac{1}{2x\ln \left(10\right)+\frac{\ln \left(10\right)}{x-1}+\ln \left(10\right)}\right)+\frac{\log _{10}\left(\frac{x}{\sqrt{1-2x}}\right)\tan \left(x\right)}{\cos \left(x\right)}\right) \\
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More