Question

If y = cos⁻¹ [sin (4^x)], find `("d"y)/("d"x)`

Answer 1

y = cos⁻¹ [sin (4^x)]

= `cos^-1 [cos(pi/2 - 4^x)]`

= y = `pi/2 - 4^x`

Differentiating w.r.t. x, we get

`("d"y)/("d"x) = "d"/("d"x)(pi/2 - 4^x)`

= 0 – 4^x log 4

= – 4^x log 4