Question

how to differentiate sqrt((secx)^2+(csc x)^2) with respect to x, to get the answer as -4 |cosec 2x| cot 2x

Answer 1

use sec^2x=1/cos^2x
cosec^2x=1/sin^2x

Answer 2

@shamim could you show a few steps?

Answer 3

√(sec^2x+cpsec^2x)
√((1/cos^2x)+(1/sin^2x))
√((cos^2x+sin^2x)/cos^2x.sin^2x)
√(1/sin^2x.cos^2x)
1/(sinx.cosx
2/(2.sin x.cos x)
2/sin2x
2 cosec2x

Answer 4

then take derivative of csc x ,
csc x -> - csc x cot x

Answer 5

√(sec^2(x)+csc^2(x))
√((1/cos^2(x))+(1/sin^2(x)))
√( (cos^2x+sin^2x)/(cos^2(x).sin^2(x)) )
√( 1/(sin^2(x).cos^2(x)) )
1/|(sinx.cosx|
2/(2|sin x.cos x|)
2/|sin(2x)|
2 |csc(2x)|

Answer 6

i dont think the absolute value will affect the derivative much, but it might

Answer 7

@perl how do we differentiate 2 |csc(2x)| to get -4 |cosec 2x| cot 2x