Question

find dr/dx
for r= tanxsecx

What is the rule to solve this problem?
How do you solve it?

Answer 1

I go the answer sec^3xtanx

Answer 2

Ahh...you would be right...lol

Answer 3

wanted to know how to change the answer to (sin^2(x)+1) sec^3(x)

Answer 4

Product rule.

Write down tanx, differentiate secx + write down secx, differentiate tanx .

Hope this helps!

Answer 5

\[ r'= (tanx)' sec x + (sec x)' tan x\\\huge= sec^3 x + sec^2x tanx = sec^3x ( 1 + \frac{tan x}{secx})\]
and \(sec x =\dfrac {1}{cos x}\rightarrow \dfrac{1}{sec x}= cos x\) replace to above
\[\huge sec^3 x(1 + tanx cox x)= sec^3 x (1 + sinx)\] cannot = \(sec^3 x ( 1 + sin^2x)\)