The derivative of ${a^{\sec x}}{\rm{w}}{\rm{.r}}{\rm{.t}}{\rm{.}}{a^{\tan x}}(a > 0)$ is

$\sin x{\rm{ }}{a^{\sec x - \tan x}}$

$\sec x{\rm{ }}{a^{\sec x - \tan x}}$

$\sin x{\rm{ }}{a^{\tan x - \sec x}}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

The derivative of

{a^{\sec x}}\mathrm{w}\mathrm{.r}\mathrm{.t}\mathrm{.}{a^{\tan x}}(a > 0)

View answer and explanation

Correct option: C

\sin x\mathrm{ }{a^{\sec x - \tan x}}

Option C (

\sin x\mathrm{ }{a^{\sec x - \tan x}}

) is correct because after applying the chain rule and simplifying, the derivative of

{a^{\sec x}}

with respect to

{a^{\tan x}}

\sin x\mathrm{ }{a^{\sec x - \tan x}}

Practice All Chapter MCQs →

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x

y

x>0

x y=1

x+y

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[x]

x

x=k, k

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\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

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v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}