Which of the following is/are true? I. The derivative of $f(x)=\sin 2 x$ is $2\left(\cos ^2 x-\sin ^2 x\right)$. II. The derivative of $g(x)=\cot x$ is $-\operatorname{cosec}^2 x$.

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

Which of the following is/are true?

I. The derivative of

f(x)=\sin 2 x

2\left(\cos ^2 x-\sin ^2 x\right)

.

II. The derivative of

g(x)=\cot x

-\operatorname{cosec}^2 x

View answer and explanation

Correct option: A

Both I and II are true

Option A is correct because both statements are true. The derivative of sin(2x) is indeed 2(cos²x - sin²x), and the derivative of cot(x) is -cosec²(x).

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and

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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}}

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

is equal to If

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

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