#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# differentiate with respect to xe^sin x + (tan x)^x

Arun Kumar IIT Delhi
6 years ago

Hello Student,
$\\ \\ \frac{d}{dx}\left(e^{\sin \left(x\right)}+\tan ^x\left(x\right)\right) \\ =\frac{d}{dx}\left(e^{\sin \left(x\right)}\right)+\frac{d}{dx}\left(\tan ^x\left(x\right)\right) \\ \frac{d}{dx}\left(e^{\sin \left(x\right)}\right) \\ =\frac{d}{du}\left(e^u\right)\frac{d}{dx}\left(\sin \left(x\right)\right) \\ \frac{d}{dx}\left(\sin \left(x\right)\right) \\ =\cos \left(x\right) \\ =e^{\sin \left(x\right)}\cos \left(x\right) \\ \frac{d}{dx}\left(\tan ^x\left(x\right)\right)$
$\\ =\frac{d}{du}\left(e^u\right)\frac{d}{dx}\left(x\ln \left(\tan \left(x\right)\right)\right) \\ \frac{d}{dx}\left(x\ln \left(\tan \left(x\right)\right)\right) \\ =\frac{d}{dx}\left(x\right)\ln \left(\tan \left(x\right)\right)+\frac{d}{dx}\left(\ln \left(\tan \left(x\right)\right)\right)x \\ =\frac{x}{\cos ^2\left(x\right)\tan \left(x\right)}+\ln \left(\tan \left(x\right)\right) \\ =e^{x\ln \left(\tan \left(x\right)\right)}\left(\frac{x}{\cos ^2\left(x\right)\tan \left(x\right)}+\ln \left(\tan \left(x\right)\right)\right) \\ =e^{\sin \left(x\right)}\cos \left(x\right)+\tan ^x\left(x\right)\left(\frac{x}{\cos ^2\left(x\right)\tan \left(x\right)}+\ln \left(\tan \left(x\right)\right)\right) \\$

Thanks & Regards
Arun Kumar
Btech, IIT Delhi