Find the derivatives of the following : (i) `(x^(3)3x^(2)+4)(4x^(5)+x^(2)-1)` (ii) `(9x^(2))/(x-3)`
Text Solution
AI Generated Solution
To find the derivatives of the given functions, we will use the product rule for the first function and the quotient rule for the second function.
### Part (i): Find the derivative of \( (x^3 + 4)(4x^5 + x^2 - 1) \)
1. **Identify the functions**:
Let \( u = x^3 + 4 \) and \( v = 4x^5 + x^2 - 1 \).
2. **Find the derivatives of \( u \) and \( v \)**:
...
Topper's Solved these Questions
BASIC MATHS
ALLEN|Exercise EXERCISE-1|128 Videos
BASIC MATHS
ALLEN|Exercise EXERCISE-2|80 Videos
AIIMS 2019
ALLEN|Exercise PHYSICS|40 Videos
CIRCULAR MOTION
ALLEN|Exercise EXERCISE (J-A)|6 Videos
Similar Questions
Explore conceptually related problems
Find the derivatives of the following : f(x)=(x^(3)-3x^(2)+4)(4x^(5)+x^(2)-1) .
Find the derivatives of the following : f(x)=(3x+2)/((x+5)(2x+1)+3)
Find the derivatives of the following (1-3) functions : f(x)=x^(3)+4x^(2)+3x+2
Find the derivative of the following w.r.t.x (i) (7x8)^(4)*(5x-1)^(3)( ii) (2x+1)^(4)*(2x^(2)+7x) (iii) (x+1)*(2x+2)*(2x^(2)+3)
Differentiate the following with respect to x. (i) (x^3 +2x^2 - 4)(4x^5 - x^2 +1) (ii) (7x^5)/(x+3)
Find the product of the following binomials; (x^(4)+(2)/(x^(2)))(x^(4)-(2)/(x^(2)))( ii) (x^(3)+(1)/(x^(3)))(x^(3)-(1)/(x^(3)))
Find the derivative of the following functions w.r.t x (i) sqrt(3x -2) for x gt 2/3 (ii) (2x^(2) +3)^(5/3) (x+5)^(-1/3)
Find the derivative of (x^(3) - 3x^(2) + 4)(4x^(5) + x^(2) -1) :
Obtain the different coefficient of the following : (i) (x-1)(2x+5) (ii) (1)/(2x+1) (iii) (3x+4)/(4x+5) (iv) (x^(2))/(x^(3)+1)