Question

Differentiate sec2 (x2) with respect to x2.​

Answer 1

Solution

Derivative of y is 2sec²(x²)tan(x²)

Given

Let y = sec²(x²)

→ y = sec(x²) . sec(x²) = uv

To finD

Derivative of y

Using Product Rule,

y' = u'v + v'u

→ y' = [tan(x²)sec(x²)]sec(x²) + [tan(x²)sec(x²)]sec(x²)

→ y' = sec²(x²)tan(x²) + sec²(x²)tan(x²)

→ y' = 2sec²(x)²tan(x²)

Answer 2

$\huge\bold{Question}$

Differentiate sec² (x²) with respect to x²

$\huge\bold{Answer}$

Let sec²(x²) = y

y = sec(x²) × sec(x²) = uv

According to the question we have to find Derivative of y

Simply by using product rule formula :-

= y' = u'v + v'u

= y' = {tan(x²)sec(x²)}sec(x²) + {tan(x²)sec(x²)}sec(x²)

= y' = sec²(x²)tan(x²) + sec²(x²)tan(x²)

= y' = 2sec²(x)²tan(x²)

Hence the differentiation of sec² (x²) w.r.t x² is 2sec²(x)²tan(x²)