Home
Class 11
MATHS
For some constants a and b, find the der...

For some constants a and b, find the derivative of (i) `(x" "" "a)" "(x" "" "b)` (ii) `(a x^2+b)^2` (iii) `(x-a)/(x-b)`

Text Solution

Verified by Experts

Let `y=(x-a)(x-b)`
`rArr (dy)/(dx)=(d)/(dx)[(x-a)(x-b)]`
`=(x-a)(d)/(dx)(x-b)+(x-b)(d)/(dx)(x-a)`
`=(x-a)(1-0)+(x-b)(d)/(dx)(x-a)`
`=(x-a)(1-0)+(x-b)(1-0)`
`=x-a+x-b=2x- a-b`
(ii) Let `y=(ax ^(2)+b)^(2)`
`=a^(2)x^(4)+2abx^(2)+b^(2)`
`rArr(dy)/(dx)=(d)/(dx)(a^(2)x^(4)+2abx^(2)+b^(2))`
`=a^(2)(d)/(dx)x^(4)+2ab(d)/(dx)x^(2)+(d)/(dx)b^(2)` ltb rgt `=4a^(2)x^(3)+4abx`
(iii) Let `y=(x-a)/(x-b)`
`rArr (dy)/(dx)=(d)/(dx)((x-a)/(x-b))`
`=((x-b)(d)/(dx)(x-a)-(x-a)(d)/(dx)(x-b))/((x-b)^(2))`
`=((x-b).1-(x-a).1)/((x-b)^(2))=(a-b)/((x-b)^(2))`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|30 Videos

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise EX -13.1|32 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|6 Videos

  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|14 Videos

Similar Questions

Explore conceptually related problems

Find the derivative (i) x^(1//3) (ii) (2)/(x^(3//2)) (iii) 3x^(-1//4)

If x = (2ab)/(a + b) , find the value of : (x + a)/(x - a) + (x + b)/(x - b) .

Find the derivative of the function f(x)=x^3-6x^2+a x+b

Evaluate : (i) (a+6b)^(2) " " (ii) (3x-4y)^(2) " " (iii) (2a-b+c)^(2)

Find the product. (i) (5-2x)(3+x) (ii) (x+7y)(7x-y) (iii) (a^2+b)(a+b^2) (iv) (p^2-q^2)(2p+q)

Expand : (i) (3a-5b)^(2) " " (ii) (a+(1)/(a))^(2) " " (iii) (2x-(1)/(2x))^(2) .

Find the derivative of function 3a x^2+2b x+c=y with respect to x

Find the derivative of (x^(n)-a^(n))/(x-a) at x=a for some constant a.

Find the derivative of the following function with respect to 'X' (i) x^(4) (ii) x^(-3) (iii) 3x^(2)

If f(x)=(x-a)^2(x-b)^2 , find f(a+b)