Could someone please answer the differentiation of sec^2x.tan x
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The derivative of y=sec2x+tan2x is:
4sec2xtanx
Process:
Since the derivative of a sum is equal to the sum of the derivatives, we can just derive sec2x and tan2x separately and add them together.
For the derivative of sec2x, we must apply the Chain Rule:
F(x)=f(g(x))
F'(x)=f'(g(x))g'(x),
with the outer function being x2, and the inner function being secx. Now we find the derivative of the outer function while keeping the inner function the same, then multiply it by the derivative of the inner function. This gives us:
f(x)=x2
f'(x)=2x
g(x)=secx
g'(x)=secxtanx
Plugging these into our Chain Rule formula, we have:
F'(x)=f'(g(x))g'(x),
F'(x)=2(secx)secxtanx=2sec2xtanx
Now we follow the same process for the tan2xterm, replacing secx with tanx, ending up with:
f(x)=x2
f'(x)=2x
g(x)=tanx
g'(x)=sec2x
F'(x)=f'(g(x))g'(x),
F'(x)=2(tanx)sec2x=2sec2xtanx
Adding these terms together, we have our final answer:
2sec2xtanx+2sec2xtanx
= 4sec2xtanx
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sec^2x.tan x
Ask for details FollowReport bySruthypotter3714 26.12.2018
Answers

Aman17h
is writing an answer

Rrjack29 Physics Newton
The derivative of y=sec2x+tan2x is:
4sec2xtanx
Process:
Since the derivative of a sum is equal to the sum of the derivatives, we can just derive sec2x and tan2x separately and add them together.
For the derivative of sec2x, we must apply the Chain Rule:
F(x)=f(g(x))
F'(x)=f'(g(x))g'(x),
with the outer function being x2, and the inner function being secx. Now we find the derivative of the outer function while keeping the inner function the same, then multiply it by the derivative of the inner function. This gives us:
f(x)=x2
f'(x)=2x
g(x)=secx
g'(x)=secxtanx
Plugging these into our Chain Rule formula, we have:
F'(x)=f'(g(x))g'(x),
F'(x)=2(secx)secxtanx=2sec2xtanx
Now we follow the same process for the tan2xterm, replacing secx with tanx, ending up with:
f(x)=x2
f'(x)=2x
g(x)=tanx
g'(x)=sec2x
F'(x)=f'(g(x))g'(x),
F'(x)=2(tanx)sec2x=2sec2xtanx
Ask for details FollowReport bySruthypotter3714 26.12.2018
Answers

Aman17h
is writing an answer

Rrjack29 Physics Newton
The derivative of y=sec2x+tan2x is:
4sec2xtanx
Process:
Since the derivative of a sum is equal to the sum of the derivatives, we can just derive sec2x and tan2x separately and add them together.
For the derivative of sec2x, we must apply the Chain Rule:
F(x)=f(g(x))
F'(x)=f'(g(x))g'(x),
with the outer function being x2, and the inner function being secx. Now we find the derivative of the outer function while keeping the inner function the same, then multiply it by the derivative of the inner function. This gives us:
f(x)=x2
f'(x)=2x
g(x)=secx
g'(x)=secxtanx
Plugging these into our Chain Rule formula, we have:
F'(x)=f'(g(x))g'(x),
F'(x)=2(secx)secxtanx=2sec2xtanx
Now we follow the same process for the tan2xterm, replacing secx with tanx, ending up with:
f(x)=x2
f'(x)=2x
g(x)=tanx
g'(x)=sec2x
F'(x)=f'(g(x))g'(x),
F'(x)=2(tanx)sec2x=2sec2xtanx
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