The differential for each function can be found:(a)y=x2sin⁡(4x)dy=(b)y=ln⁡((1+t2))dy=

Fallbasiss4

Fallbasiss4

Answered

2022-01-23

The differential for each function can be found:
(a)y=x2sin(4x) 
 dy = 
(b)y=ln((1+t2)) 
 dy =

Answer & Explanation

dodato0n

dodato0n

Expert

2022-01-24Added 9 answers

a) Given function is
y=x2sin4x
Here, we use product rule of differentiation to find the differential
dy=(sin4x)d(x2)+x2d(sin4x)
Differential of x2 is 2xdx and that of sin4x is 4cos4x
dy=(2xsin4x)dx+(4x2cos4x)dx
dy=(2xsin4x+4x2cos4x)
Hana Larsen

Hana Larsen

Expert

2022-01-25Added 17 answers

b) Given function is
y=ln1+t2
Firstly, we apply rule of logarithms logmn=nlogm
y=ln1+t2
y=ln(1+t2)12
y=12ln(1+t2)
Differential of logx is dxx and that of x2 is 2xdx
dy=121(2+t2)d(1+t2)
dy=12(1+t2)2tdt
dy=t(1+t2)dt

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