JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Which of the following is/are true?

I. The derivative of

\sin (x+a)

\cos (x+a)

, where

a

is a fixed non-zero constant.

II. The derivative of

\operatorname{cosec} x \cot x

\operatorname{cosec}^3 x-\cot ^2 x \operatorname{cosec} x

View answer and explanation

Correct option: B

Only I is true

Option B (Only I is true) is correct because the derivative of sin(x+a) is cos(x+a), while the derivative of cosec(x)cot(x) is -cosec³(x) - cot²(x)cosec(x).

More Questions from DIFFERENTIATION

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f(x)=|x|^{|\tan x|}

, then

f^{\prime}\left(\frac{-\pi}{6}\right)

is equal to Let

x

and

y

be two real numbers such that

x>0

and

x y=1

. The minimum value of

x+y

is Let

f(x)=[x] \sin (\pi x)

where

[x]

denotes the integer part of

x

. Then at

x=k, k

being an integer, the left derivative of

f(x)

is If

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

then

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

is equal to

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

is equal to If

z = y + f\left( v \right),

where

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

then

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