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

Differentiate the following:

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

Sum

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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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 8 | Page 163

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

y = sin x + cos x

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g(t) = t³ cos t

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g(t) = 4 sec t + tan t

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y = x sin x cos x

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y = (x² + 4x + 6)⁵

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y = 4 sec 5x

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y = `x^(cosx)`

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y = `x^(logx) + (logx)^x`