Chain Rule of Differentiation
Trending Questions
Q.
If and , then
None of these
Q.
Let f:→R→R, g:R→R and h:R→R be differentiable functions such that f(x)=x3+3x+2, g(f(x))=x and h(g(g(x)))=x for all x ε R. Then
g′(2)=115
h′(1)=666
h(0)=16
h(g(3))=36
Q. limx→0(1x+2x+3x+....+nxn)1x is equal to
- (n!)1n
- n!
- ln(n!)
- (n!)n
Q. Let f:R→R be a function defined by f(x+1)=f(x)−5f(x)−3 ∀ x∈R then which of the following statements are true?
- f(7)=f(10)
- f(2017)=f(2020)
- f(2021)=f(2025)
- f(2018)=f(2026)
Q.
If y=[x+√x2+a2]n, then dydx is equal to
ny√x2+a2
−ny√x2+a2
nx√x2+a2
−nx√x2+a2
Q. limx→0(1x+2x+3x+....+nxn)1x is equal to
- (n!)n
- (n!)1n
- n!
- ln(n!)
Q. If f(1)=1, f′(1)=3, then the derivative of f(f(f(x)))+(f(x))2 at x=1 is :
- 9
- 12
- 15
- 33
Q. If f(x)=(logcotxtan x)(logtanxcot x)−1+tan−1(x√(4−x2)) then f'(0) is equal to
- −2
- 2
- 12
- 0
Q. Derivative of y=(sin x)2 with respect to x will be
- 2sinx
- (cosx)2
- 2sinxcosx
- None of the above
Q. Let f be a function satisfying f(x)+f(x+5)=0. If fundamental period of f(x) is T, then T is equal to
Q. Let F(x)=[g(x)−g(−x)f(x)+f(−x)]m such that m=2n, n∈N and f(−x)≠−f(x); g(−x)≠−g(x) then F(x) is
- an odd function
- an even function
- neither odd nor even function
- both even and odd function
Q. Let f be a differentiable function such that
f(1)=2 and f′(x)=f(x) for all x∈R. If h(x)=f(f(x)), then h′(1) is equal to :
f(1)=2 and f′(x)=f(x) for all x∈R. If h(x)=f(f(x)), then h′(1) is equal to :
- 2e2
- 4e
- 2e
- 4e2
Q. Let f:R→R, g:R→R and h:R→R be differentiable functions such that f(x)=x3+3x+2, g(f(x))=x and h(g(g(x)))=x for all x∈R. Then
- g′(2)=115
- h′(1)=666
- h(0)=16
- h(g(3))=36
Q. Let f:R→R be f(x)=x3+x2+x−1 and g(x)=f−1(x), then g′(2) is
- 2
- 6
- 16
- 12
Q. Derivative of ln(x3)×(x3)(2)x at x = 1 is
- 1
- 1.5
- 3
Q. Suppose f and g are differentiable functions on (0, ∞) such that f'(x)=−g(x)x and g'(x)=−f(x)x, for all x>0. Further, f(1)=3 and g(1)=−1.
If f(x)+g(x)=Axk, for all x>0 and some constant A, then the value of k equals
If f(x)+g(x)=Axk, for all x>0 and some constant A, then the value of k equals
- 1
- 2
- −1
- −2
Q. If f(x)=√x2+6x+9, then f '(x) is equal to
- 1 for x>−3
- −1for x<−3
- 1 for all x∈R
- 0 for x=−3
Q. If (sin−1x)2−(cos−1x)2=a ; 0<x<1, a≠0, then the value of 2x2−1 is:
- cos(2aπ)
- sin(4aπ)
- cos(4aπ)
- sin(2aπ)
Q.
If g is the inverse of a function f and f′(x)=11+x5, then g′(x) is equal to:
11+{g(x)}5
1+{g(x)}5
1+x5
5x4
Q. The range of f(x)=sin2x−2sinx is
- (0, 3)
- [−1, 3)
- [0, 3]
- [−1, 3]
Q.
Let f(x)=ex+sinx and g(x)=f−1(x), h(x)=g(x)+g′(x) then 4h(1) is :
Q.
If 2x=y1/5+y−1/5 then (x2−1)d2ydx2+xdydx=
5y
25y
25 y2
y + 25
Q.
If g is the inverse of a function f and f′(x)=11+x5, then g′(x) is equal to:
11+{g(x)}5
1+{g(x)}5
1+x5
5x4
Q. Let f:R→R be f(x)=x3+x2+x−1 and g(x)=f−1(x), then g′(2) is
- 2
- 6
- 16
- 12
Q. Let y=f(x) is a positive function which satisfies equation √y2+2x+√y2−2x=2x2, then dydx is
- 2x3−x−3y
- 2x4−x−2y
- 2x4−x−2√x6+1
- 2x3−x−3√1+x6
Q. Let f and g be two differentiable functions such that f′(x)=ϕ(x) and ϕ′(x)=f(x) for all real x. If f(3)=5 and f′(3)=4, then the value of (f(10))2−(ϕ(10))2 is