Differentiate the following: f(x) = x7-3x

Differentiate the following:

f(x) = `x/sqrt(7 - 3x)`

Sum

f(x) = `x/sqrt(7 - 3x)`

= `x/(7 - 3x)^(1/2)`

f'(x) = `((7 - 3x)^(1/2) xx 1 - x xx 1/2 (7 - 3x)^(1/2 - 1) (- 3))/[(7 - 3x)^(1/2)]^2`

= `((7 - 3x)^(1/2) + 3/2 xx (7 - 3x)^(- 1/2))/((7 - 3x))`

= `((7 - 3)^(1/2) + (3x)/(2(7 - 3x)^(1/2)))/((7 - 3x))`

= `(((7 - 3x)^(1/2) xx 2(7 - 3x)^(1/2) + 3x)/(2(7 - 3x)^(1/2)))/((7 - 3x))`

= `(2(7 - 3x) + 3x)/(2(7 - 3x)^(1/2) (7 - 3x))`

= `(14 - 6x + 3x)/(2(7 - 3x)^(3/2)`

f'(x) = `(14 - 3x)/(2(7 - 3x)^(3/2)`

shaalaa.com

Differentiation Rules

Is there an error in this question or solution?

Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [Page 163]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 17 | Page 163

Find the derivatives of the following functions with respect to corresponding independent variables:

y = sin x + cos x

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `(tanx - 1)/secx`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = e^-x . log x

Differentiate the following:
y = `root(3)(1 + x^3)`

Differentiate the following:
F(x) = (x³ + 4x)⁷

Differentiate the following:

s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`

Differentiate the following:
y = `sqrt(x +sqrt(x)`

Differentiate the following:
y = `sin(tan(sqrt(sinx)))`

Differentiate the following:

y = `sin^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:
y = `x^(cosx)`

Find the derivatives of the following:
y = `x^(logx) + (logx)^x`