wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the derivative with respect to x of the function (logcosxsinx)(logsinxcosx)1+sin12x1+x2 at x=π4

A
8(4π2+161log2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
8(4(π+4)21log2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
8(4π2+16+1log2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
8(4(π+4)21log2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 8(4π2+161log2)
Let y=(logcosxsinx)(logsinxcosx)1+sin12x1+x2

=(logcosxsinx)2+2tan1x[logba=1logab] =(logesinxlogecosx)2+2tan1x.

dydx=2(logsinxlogcosx)cotx.logcosx+tanxlogsinx(logcosx)2+21+x2

Hence at x=π4.

we have dydx=2.log(1/2)log(1/2)1.log(1/2)+1.log(1/2)[log(1/2)]2+21+(π2/16)=8log2+32π2+16

=8(4π2+161log2).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Logarithmic Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon