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)`

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Differentiation Rules

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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:

f(x) = x – 3 sin x

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

y = e^x sin x

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

y = sin x⁰

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

Draw the function f'(x) if f(x) = 2x² – 5x + 3

Differentiate the following:
y = (2x – 5)⁴ (8x² – 5)^–3

Differentiate the following:
y = tan (cos x)

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

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

Find the derivatives of the following:

(cos x)^{log x}