Home
Class 11
MATHS
Find the derivatives of (i) x^(9) , (...

Find the derivatives of
(i) `x^(9)` , (ii) `x^(-3)` , (iii)` 3sqrt(x)` , (iv) `1/(sqrt(x))`

Text Solution

AI Generated Solution

To find the derivatives of the given functions, we will use the power rule of differentiation, which states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \). Let's solve each part step by step: ### (i) Find the derivative of \( x^9 \) 1. **Identify the exponent**: Here, \( n = 9 \). 2. **Apply the power rule**: ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Solved Examples|48 Videos

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exrescise 28A|13 Videos

  • CONDITIONAL IDENTITIES INVOLVING THE ANGLES OF A TRIANGLE

    RS AGGARWAL|Exercise EXERCISE 16|12 Videos

  • ELLIPSE

    RS AGGARWAL|Exercise EXERCISE|26 Videos

Similar Questions

Explore conceptually related problems

Find the derivative of (i) 8x^(3) , (ii) 6sqrt(x) , (iii) 5e^(x) , (iv) 9 xx 2^(x)

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

Find the derivative of the following functions (i) x^(3) + cos x + sqrt(x) (ii) (sqrt(x) + 1)^(2) (iii) (x^(2) + 2x - 3)(x + 1)

Find the second derivative of : (i) x^(11)" "(ii)5^(x)" "(iii)tanx" "(iv)cos^(-1)x

Find the derivative of (i)2x-(3)/(4) (ii) (5x^(3)+3x-1)(x-1) (iii) x^(-3)(5+3x)

Integrate with respect to x: i) sin^(2)x , ii) cos^(3)x , iii) sin2xcos3x , iv) 1/(sqrt(x+3)-sqrt(x+2))

Find periods for {:((i) cos^(4)x., (ii) sin^(3)x., (iii)cos sqrt(x).,(iv) cos x.):}

Find the derivative of the following functions. (i) (x^(2) tan x) (ii) (x + cos x) (sqrt(x) + 1) (iii) x^(-3) (e^(x) + 5 "sin" x)

Differentiate the following function : (i) (x^(2) - 5x + 6)(x-3) , (ii) (sqrt(x) + 1/(sqrt(x)))^(2) , (iii) (3x^(2) + 2x + 5)/(sqrt(x))

Which of the following are polynomials : (i) 3x^(2)-7x+6 " " (ii) x^(2)-sqrt(3)x+4 " " (iii) 3sqrt(x)+5 " " (iv) 13 " " (v) a+(5)/(a)+6