1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If fn(x)=efn−1(x) for all nϵN and f0(x)=x then ddx{fn(x)} is equal to

A
fn(x).ddx{fn1(x)}
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
fn(x).fn1(x)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
fn(x).fn1(x)....f2(x).f1(x)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct options are A fn(x).ddx{fn−1(x)} C fn(x).fn−1(x)....f2(x).f1(x)Given: fn(x)=efn−1(x) Consider, ddx{fn(x)}=ddxefn−1(x)=efn−1(x)ddx(fn−1(x))=fn(x)ddx(fn−1(x))=fn(x)ddxefn−2(x)=fn(x)efn−2(x)ddxfn−2(x)=fn(x)fn−1(x)ddxfn−2(x)Continuing this process, we getddx{fn(x)}=fn(x)fn−1(x)fn−2(x)....f1(x)ddxf0(x)Hence, ddx{fn(x)}=fn(x)fn−1(x)fn−2(x)....f1(x)

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Basic Theorems in Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program