Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Differentiate each of the following w.r.t. x sin root x + cos^2 rootx

Differentiate each of the following w.r.t. x
\sin \sqrt{x}+\cos ^{2} \sqrt{x}

Answers (1)

Given:

\sin \sqrt{x}+\cos ^{2} \sqrt{x}

We have \sin \sqrt{x}+\cos ^{2} \sqrt{x}

y=\sin \sqrt{x}+\cos ^{2} \sqrt{x}

Differentiate w.r.t x

\\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{d} \mathrm{x}}\left(\sin (\mathrm{x})^{\frac{1}{2}}+\left(\cos \mathrm{x} ^\frac{1}{2}\right)^{2}\right) \\ \frac{\mathrm{dy}}{\mathrm{dx}}=\left(\frac{\mathrm{d}}{\mathrm{d} \mathrm{x}}\left(\sin (\mathrm{x})^{\frac{1}{2}}\right)+\frac{\mathrm{d}}{\mathrm{dx}}\left(\left(\cos \mathrm{x}^{\frac{1}{2}}\right)^{2}\right)\right) \\ \frac{\mathrm{dy}}{\mathrm{dx}}=\left(\frac{1}{2 \sqrt{\mathrm{x}}} \cdot \cos \sqrt{\mathrm{x}}+2 \cos \sqrt{\mathrm{x}}\left[-\sin \sqrt{\mathrm{x}} \cdot \frac{1}{2 \sqrt{\mathrm{x}}}\right]\right) \\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2 \sqrt{\mathrm{x}}}[\cos (\sqrt{\mathrm{x}})-\sin (2 \sqrt{\mathrm{x}})]

 

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question