Question

Could someone please answer the differentiation of sec^2x.tan x

Answer 1

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

Answer 2

sec^2x.tan x

Ask for details FollowReport bySruthypotter3714 26.12.2018

Answers



Aman17h

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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