Derivatives of Composite and Implicit Functions

IMPORTANT

Derivatives of Composite and Implicit Functions: Overview

This Topic covers sub-topics such as Differentiation of Implicit Functions, Derivative of Inverse Function, Differentiation of Inverse Trigonometric Functions and, Chain Rule for Differentiation of Composite Functions

Important Questions on Derivatives of Composite and Implicit Functions

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

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

HARD
IMPORTANT

Find the derivative with respect to x of the function :

logcosxsinxlogsinxcosx-1+arcsin2x1+x2 at x=π4

HARD
IMPORTANT

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

MEDIUM
IMPORTANT

If   siny=xsin(a+y),  find   dy dx

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

Let f(x)=x+cosx+2 and gx be the inverse function of fx, then g'3 is equal to

MEDIUM
IMPORTANT

Suppose, the function fx-f2x has the derivative 5 at x=1 and derivative 7 at x=2, the derivative of the function fx-f4x at x=1 has the value 10+λ, then the value of λ is equal to:

MEDIUM
IMPORTANT

If y=4-x4-x-6-xx-64-x+x-6, then dydx is equal to

MEDIUM
IMPORTANT

Differentiate the following w.r.t x:

cos-11+x2

MEDIUM
IMPORTANT

The derivative of the function cos11+x2 is

HARD
IMPORTANT

Differentiate tan-11-sin4x1+sin4x w.r.t x.

EASY
IMPORTANT

Differentiation of log(secx+tanx) w.r.t. x is

EASY
IMPORTANT

Differentiation of sinx2+x w.r.t. x is