Question

Find the derivative of tan(2x + 3) with respect to x ?
1. 2 sec²(2x + 3)
2. 3 sec2(2x + 3)
3. cosec²(2x + 3)
4. None of these

Answer 1

Correct Answer - Option 1 : 2 sec²(2x + 3)

CONCEPT:

• \(\frac{{d\left( {\tan x} \right)}}{{dx}} = {\sec ^2}x\)

• Let y = f(v) be a differentiable function of v and v = g(x) be a differentiable function of x then \(\frac{{dy}}{{dx}} = \frac{{dy}}{{dv}} \cdot \frac{{dv}}{{dx}}\)

CALCULATION:

Let y = tan(2x + 3)

Here, we have to find dy/dx

As we know that, \(\frac{{d\left( {\tan x} \right)}}{{dx}} = {\sec ^2}x\)

⇒ \(\frac{dy}{dx} = sec^2(2x + 3) \cdot \frac{d(2x +3)}{dx}\)

⇒ \(\frac{dy}{dx} = 2 sec^2(2x + 3)\)

Hence, the correct answer is option 1.