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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)

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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).

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