Question

Find the differentiation of f(x) = x2 tan x

1.  x(xsec2x + 2tan x)
2.  (xsec2x + 2tan x)
3. xsec2x
4.  x(x + 2tan x)

Answer 1

Correct Answer - Option 1 :  x(xsec2x + 2tan x)

Concept:

• \(\rm d\over dx\)xn = nxn-1
• \(\rm d\over dx\)sin x = cos x
• \(\rm d\over dx\)cos x = -sin x
• \(\rm d\over dx\)ex = ex
• \(\rm d\over dx\)ln x = \(\rm1\over x\)
• \(\rm d\over dx\)tan x = sec2 x
• \(\rm d\over dx\)[f(x)g(x)] = g(x)\(\rm d\over dx\)f(x) + f(x)\(\rm d\over dx\)g(x)

Chain Rule: If y is a function of u and u is a function of x

• \(\rm {dy\over dx} = {dy\over du}\times {du\over dx}\)

Calculation:

f(x) = x2 tan x

f'(x) = \(\rm d\over dx\)f(x) = \(\rm d\over dx\)(x2 tan x)

f'(x) = tan x \(\rm d\over dx\)(x2) + x2 \(\rm d\over dx\)tan x

f'(x) = tan x (2x) + x2 (sec² x)

f'(x) = x(xsec2x + 2tan x)

∴ The required value is  x(xsec2x + 2tan x).