Question

Differentiate w.r.t. x
(1) d sin³x/dx

(2) d tan(x^n)/ dx

(3) d tan(x°)/dx

Answer 1

Answer :

(1)

Now,

d/dx (sin³x)

= 3 sin³⁻¹x d/dx (sinx)

= 3 sin²x cosx,

which is the required derivative.

(2)

Now,

d/dx (tan xⁿ)

= (sec² xⁿ) d/dx (xⁿ)

= n xⁿ⁻¹ (sec² xⁿ),

which is the required derivative.

(3)

We know that, 180° = πᶜ

∴ x° = (πx/180)ᶜ

Now,

d/dx (tan x°)

= d/dx (tan πx/180)

= (π/180) sec²(πx/180)

= (π/180) sec²x°,

which is the required derivative.

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