Home
Class 11
PHYSICS
Find (dy)/(dx) for the following : (i)...

Find `(dy)/(dx)` for the following :
(i) `y=x^(7//2)` (ii) `y=x^(-3)`
`(iii) y=x` (iv) `y=x^(5)+x^(3)+4x^(1//2)+7`
(v) `y=5x^(4)+6x^(3//2)+9x` (vi) `y=ax^(2)+bx+C`
`(Vii) `y=3x^(5)-3x-1/x`

Text Solution

Verified by Experts

The correct Answer is:
(i) `(7)/(2)x ^(5//2)`
(ii) `-3x^(-4)`
(iii) 1
(iv) `5x^(4) + 3x^(2) + 2x^(-1//2)`
(v) `20 x^(3) + 9 x^(1//2) + 9`
(vi) `2ax+b`
(vii) `15x^(4) - 3+ (1)/(x^(2)) `
(i) `y = x^(7//2)`
`(dy)/(dx) = (d)/(dx)(x^(7//2)) = (7)/(2) x^((7)/(2) -1) = (7)/(2) x^(5//2) `
(ii) `y= x^(3)" "therefore" "(dy)/(dx) = -3x^(-4)`
(iii) `y=x" "therefore " "(dy)/(dx) = 1`
(iv) `y= x^(5) + x^(3) + 4x^(1//2) + 7`
`(dy)/(dx) = 5x^(4) + 3x^(2) + 2x^(-1//2) + 0`
`" "= 5x^(4) + 3x^(2) + 2x^(-1//2)`
(v) `y = 5x^(4) + 6x ^(3//2) + 9x `
`(dy)/(dx) = 20 x^(3) + 9x^(3//2-1) + 9`
`" "= 20 x^(3) + 9x^(1//2)+ 9`
(vi) `y= ax^(2) + bx+ c rArr (dy)/(dx) = 2ax + b`
(vii) `y= 3x^(5) - 3x- (1)/(x)`
`(dy)/(dx) = 15 x^(4)- 3+ (1)/(x^(2))`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 4|1 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 5|1 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 2|3 Videos

  • CENTRE OF MASS

    ALLEN|Exercise EXERCISE-V B|19 Videos

Similar Questions

Explore conceptually related problems

Obtian (dy)/(dx) for the following : y=5x^(4)+6x^(3//2)+9x

Find dy/dx for the following functions: y=5x^4 + 3 x^(3/2) + 6x .

Find dervatives of the following functions: (i) y=2x^(3) , (ii) y=4/x , (iii) y=3e^(x) , (iv) y=6 ln x , (v) y=5 sin x

Find (dy)/(dx) if y = 5x^(4) + 6x^(3//2) + 9x .

Find (dy)/(dx) , when (i) y= sqrtx (ii) y= x^(5) + x^(4) + 7 (iii) y=x^(2)+ 4x^(-1//2)- 3x^(-2)

Find (dy)/(dx), when (i) y=sqrt(x) (ii) y=x^(5)+x^(4)+7 (iii) y=x^(2)+4x^(-1//2)-3x^(-2)

Find the degree of each of the following polynomials : (i) 3x^(4)-x^(2)+8 " " (ii) y^(2)-5y+7 " " (iii) 3x+4 " " (iv) 3 (v) x-2x^(2)+5x^(7) " " (vi) 2y^(2)-5y^(6)+1 " "(vii) x^(3)-1 " " (viii) 3x+5x^(5)+1

Find each of the following products: (i) (4x - 7y) (4x - 7y) (ii) (3x^(2) - 4y^(2)) (3x^(2) - 4y^(2))

Find each of the following products: (i) (4x + 5y) (4x - 5y) (ii) (3x^(2) + 2y^(2)) (3x^(2) - 2y^(2))

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))