To determine
To calculate:
y'
Answer
y'=-sec21-x21-x
Explanation
Rule:
i. Power rule combined with chain rule:
ddxun=nun-1 .ddx(u)
ii. Difference rule:
ddxfx-g(x)=ddxfx-ddxgx
iii.
ddx(tanx)=sec2x
Given:
y=tan(1-x )
Calculation:
y= tan(1-x )
Let y=tanu
Where u=1-x
Differentiate y with respect to x
y'=ddxtan(1-x )
By using chain rule
y'=ddutanu.ddx(u)
By using ddx(tanx)=sec2x
y'=sec2u.ddx(u)
Substitute value of u
y'=sec21-x.ddx(1-x)
By using power rule combined with chain rule
y'=sec21-x.121-xddx(1-x)
Since by using power rule ddxx=12x
Now by using Difference rule
y'=sec21-x.121-xddx1-ddxx
Derivative of constant is zero and by using power rule
y'=sec21-x.121-x0-1
y'=sec21-x.-121-x
By rearrangement
y'=-sec21-x21-x
Conclusion:
y'=-sec21-x21-x