Question

find derivative of cos(tanx^2)​

Answer 1

Let ,

F(x) = Cos(Tan (x)²)

By using chain rule , we get

$\sf \mapsto \frac{d \{Cos(Tan {(x)}^{2} ) \}}{dx} = Sin(Tan {(x)}^{2} ) \times \frac{d(Tan {(x)}^{2} )}{dx} \\ \\ \sf \mapsto \frac{d \{Cos(Tan {(x)}^{2} ) \}}{dx} = Sin(Tan {(x)}^{2} ) \times Sec {(x)}^{2} \times \frac{d {(x)}^{2} }{dx} \\ \\ \sf \mapsto \frac{d \{Cos(Tan {(x)}^{2} ) \}}{dx} = Sin(Tan {(x)}^{2} ) \times Sec {(x)}^{2} \times 2x \\ \\ \sf \mapsto \frac{d \{Cos(Tan {(x)}^{2} ) \}}{dx} = Sin(Tan {(x)}^{2} ) \times 2xSec {(x)}^{2}$

Hence , the derivative of Cos(Tan (x)²) is Sin(Tan (x)²) × 2xSec(x)²