Derivative from First Principle
Trending Questions
Q.
Find the Derivative of Sin x.
sin x
cos x
-cos x
-sin x
Q.
Find the Derivation of f(x)=x2.at x=0
0
-1
1
2
Q.
The Derivative of ex
ex+1
xex
e2x
ex
Q. Let f:R→R be a differentiable function satisfying f(x+y)=f(x)+f(y)+xy for all x, y∈R and limh→01hf(h)=3. Which of the following statements is (are) CORRECT?
- f is a linear function
- 2f(1)=[limx→0(1+2x)1/x], where [.] denotes the greatest integer function
- The minimum value of f is −92
- f′(1)=4
Q. Let f(x)={x2sin1x, x≠00, x=0. Then
- f′ does not exist at x=0
- f′ exists and is continuous at x=0
- f′ exists but not continuous at x=0
- f′ does not exist at any point
Q. Let f be any function defined on R and let it satisfy the condition :
|f(x)−f(y)|≤|(x−y)2|, ∀ x, y∈R
If f(0)=1, then
|f(x)−f(y)|≤|(x−y)2|, ∀ x, y∈R
If f(0)=1, then
- f(x) can take any value in R.
- f(x)=0, ∀ x∈R
- f(x)>0, ∀ x∈R
- f(x)<0, ∀ x∈R
Q. Find the derivative of the following functions from first principle. (i) x 3 – 27 (ii) ( x – 1) ( x – 2) (ii) (iv)
Q. Find the derivative of cos x from first principle.
Q. Find the derivative of the following functions from first principle: (i) – x (ii) (– x ) –1 (iii) sin ( x + 1) (iv)
Q. 25. (x +cosx) (x- tanx)