Basics of Differentiation

IMPORTANT

Basics of Differentiation: Overview

This topic covers concepts, such as Basics of Differentiation, Definition of Derivative (dy/dx), Physical Interpretation of Derivative (dy/dx), Geometrical Interpretation of Derivative (dy/dx), Differentiation of Trigonometric Functions, etc.

Important Questions on Basics of Differentiation

HARD
IMPORTANT

If the dependent variable y is changed to 'z' by the substitution y = tan z then the differential equation  d 2 y d x 2 = 1 + 2 1 + y 1 + y 2 d y d x 2  is changed to d 2 z d x 2 = cos x 2 z + k d z d x 2 ,then find the value of k.

HARD
IMPORTANT

Let Px be a polynomial of degree 4 such that P1=P3=P5=P'7=0. If the real number x1,3,5 is such that Px=0 can be expressed as x=pq where 'p' and 'q' are relatively prime, then p+q equals

EASY
IMPORTANT

if y = y(x) and it follows the relation  e x y + y cos x = 2,  then find (i) y' (0) and (ii) y'' (0)

HARD
IMPORTANT

Let fx=x2-4x-3, x>2 and let gx be the inverse of fx. Find the value of g'2 where fx=2

MEDIUM
IMPORTANT

Suppose fx=tansin-12x, then f'14 is equal to

HARD
IMPORTANT

Find the derivative with respect to x of the function :

logcosxsinxlogsinxcosx-1+arcsin2x1+x2 at x=π4

MEDIUM
IMPORTANT

If y=logexex·ayyx, then dydx is equal to

HARD
IMPORTANT

If y=x22+12xx2+1+logx+x2+1, find the value of xdydx+logdydx.

HARD
IMPORTANT

If y=easin1x,1x1, then what would be the value of  (1 x 2 ) d 2 y d x 2 x dy dx a 2 y ?

MEDIUM
IMPORTANT

If (cosx)y=(siny)x, find dydx

EASY
IMPORTANT

f( x )= sinx then f'(x) equals to

MEDIUM
IMPORTANT

Evaluate [ 1 logx 1 ( logx ) 2 ] dx

MEDIUM
IMPORTANT

If y=x+x2+a2n, then dydx is

EASY
IMPORTANT

Which of the following solution is obtained when   tan x is differentiated with respect to x

EASY
IMPORTANT

y=tan1x2, then what would be the value of  x2+12d2ydx2+2xx2+1dydx

MEDIUM
IMPORTANT

If   x=a( cost+logtan t 2 ),y=asintfind d 2 y d t 2 and dy d x

EASY
IMPORTANT

On differentiating  tanx with respect to x from first principle, the solution would be:

EASY
IMPORTANT

If y=2sinx, then dydx is equal to

MEDIUM
IMPORTANT

Let h=fog, where f : RR and g : RR are differentiable functions,

If f(2)=1, f'(-1)=-2, f'(4)=3, g(2)=-1, g'(2)=4, g'(1)=8, then h'(2)=

MEDIUM
IMPORTANT

If exy-tan-1yx=2020 for x0 and y0, we get dydx=