Find the derivative of the following function-fx-x- xx-tan x

Here f(x)= (x+sec x)(x tan x) ∴ f'(x)= d/dx[(x+sec x)(x tanx)] =(x+sec x)d/dx(x tan x)+(x tan x)d/dx(x+sec x) =(x+sec x)(1 sec^2x)+(x tan x)(1+sec x tan x) ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Derivatives

Find the deri...

Question

Find the derivative of the following function:
f(x)= $(x + s e c x) (x - t a n x)$

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Solution

Here $f (x) = (x + s e c x) (x - t a n x)$

$∴ f^{'} (x) = \frac{d}{d x} [(x + s e c x) (x - t a n x)]$

$= (x + s e c x) \frac{d}{d x} (x - t a n x) + (x - t a n x) \frac{d}{d x} (x + s e c x)$

$= (x + s e c x) (1 - s e c^{2} x) + (x - t a n x) (1 + s e c x t a n x)$

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Find the derivative of the following function: f(x)= (x+sec x)(x−tan x)

Here f(x)=(x+sec x)(x−tan x) ∴f′(x)=ddx[(x+sec x)(x−tanx)] =(x+sec x)ddx(x−tan x)+(x−tan x)ddx(x+sec x) =(x+sec x)(1−sec2x)+(x−tan x)(1+sec x tan x)

Find the derivative of the following function:
f(x)= $(x + s e c x) (x - t a n x)$

Here $f (x) = (x + s e c x) (x - t a n x)$

$∴ f^{'} (x) = \frac{d}{d x} [(x + s e c x) (x - t a n x)]$

$= (x + s e c x) \frac{d}{d x} (x - t a n x) + (x - t a n x) \frac{d}{d x} (x + s e c x)$

$= (x + s e c x) (1 - s e c^{2} x) + (x - t a n x) (1 + s e c x t a n x)$