The left-hand derivative of $f(x)=[x] \sin \pi x$ at $x=k$, $k$ being an integer, is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

The left-hand derivative of

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

x=k

k

being an integer, is

View answer and explanation

Correct option: A

(-1)^k(k-1) \pi

Option A (

(-1)^k(k-1) \pi

) is correct because the left-hand derivative is computed using the limit definition and properties of the sine function near integer values.

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y

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x y=1

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[x]

x

x=k, k

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

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