Below is an attempt to derive the derivative of sec(x) using product rule, where x is in the domain of secx. In which step, if a

Question

2 months ago

14

Below is an attempt to derive the derivative of sec(x) using product rule, where x is in the domain of secx. In which step, if a

ny, does an error first appear?
Step 1:
$\sec(x) \times \cos(x) = 1$
Step 2:
$\frac{d}{dx} ( \sec(x) \times \cos(x) ) = 0$
Step 3:
$\frac{d}{dx} (\sec(x)) \times \cos(x) - \sec(x) = 0$
Step 4:
$\frac{d}{dx} \sec(x) = \frac{ \sec(x) \times \sin(x) }{ \cos(x) } = \sec(x) \times \tan(x)$

A. step 1
B. Step 2
C. Step 3
D. There is no error

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-04-01T19:57:23+03:00

tester [12.3K]2 months ago

6 0

The mistake is present in step 3. According to the product rule, we find

$\dfrac{\mathrm d}{\mathrm dx}(\sec x\times\cos x)=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x+\sec x\times\dfrac{\mathrm d}{\mathrm dx}(\cos x)$