JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

f(x)=\left|\begin{array}{ccc}x^n & \sin x & \cos x \\ n ! & \sin \frac{n \pi}{2} & \cos \frac{n \pi}{2} \\ a & a^2 & a^3\end{array}\right|

, then the value of

\frac{d^n}{d x^n}(f(x))

x=0

for

n=2 m+1

, is

View answer and explanation

Correct option: B

Option B (0) is correct because the nth derivative of f(x) at x=0 is a determinant with two identical rows, making the determinant equal to zero.

More Questions from DIFFERENTIATION

Practice All Chapter MCQs →

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

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

x

y

x>0

x y=1

x+y

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

[x]

x

x=k, k

f(x)

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],

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

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

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

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

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