Question

d/dx tanⁿx=.......,Select Proper option from the given options.
(a) ntanⁿ⁻¹x
(b) ntanⁿ⁻¹x sec²x
(c) n sec²ⁿx
(d) ntanⁿ⁻¹x secⁿ⁻¹x

Answer 1

we have to find the value of d/dx tanⁿx

we know, d(tanx)/dx = sec²x. ......(1)

and df(x)ⁿ/dx = nf(x)ⁿ⁻¹ df(x)/dx ......(2)

now, d/dx tanⁿx = ntanⁿ⁻¹x d(tanx)/dx

[from equation (2) tanⁿx = tanⁿ⁻¹x ]

= ntanⁿ⁻¹x.sec²x

[from equation (1), d(tanx)/dx = sec²x]

hence, option (b) is correct.