Differentiate the following: h(t) = tt(t-1t)32

Differentiate the following:

h(t) = `("t" - 1/"t")^(3/2)`

बेरीज

h(t) = `("t" - 1/"t")^(3/2)`

[y = f(g(x)

`("d"y)/("d"x)` = f'(g(x)) . g'(x)]

h'(t) = `3/2 ("t" - 1/"t")^(3/2 - 1) "d"/"dt" ("t" - 1/"t")`

= `3/2 (1 - 1/"t")^(1/2) [ 1 - (- 1) "t"^(-1 - 1)]`

= `3/2 ("t" - 1/"t")^(1/2) (1 + "t"^(-2))`

h'(t) = `3/2 ("t" - 1/"t")^(1/2) (1 + 1/"t"^2)`

shaalaa.com

Differentiation Rules

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६३]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 8 | पृष्ठ १६३

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 = cos x – 2 tan x

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

y = `sinx/(1 + cosx)`

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

y = x sin x cos x

Differentiate the following:
y = sin (e^x)

Differentiate the following:

y = `(x^2 + 1) root(3)(x^2 + 2)`

Differentiate the following:

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

Differentiate the following:
y = (1 + cos²)⁶

Differentiate the following:

y = `"e"^(3x)/(1 + "e"^x`

Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`

Find the derivatives of the following:

(cos x)^{log x}