Differentiate the following: f(t) = t1+tant3

Differentiate the following:

f(t) = `root(3)(1 + tan "t")`

बेरीज

f(t) = `root(3)(1 + tan "t")`

f(t) = `(1 + tan "t")^(1/3)`

[y = f(g(x)

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

`f"'"("t") = 1/3 (1 + tan "t")^(1/3 - 1) "d"/"dt" (1 + tan "t")`

= `1/3 (1 + tan "t")^(- 2/3) (0 + sec^2 "t")`

= `1/3 xx 1/(1 + tan "t")^(2/3) xx sec^2"t"`

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

`f"'"("t") = 1/2 sec^2"t" (1 + tan "t")^(- 2/3)`

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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 9 | 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:

g(t) = 4 sec t + tan t

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 = `sinx/x^2`

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

y = x sin x cos x

Differentiate the following:
y = tan 3x

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

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

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

Find the derivatives of the following:

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

Find the derivatives of the following:

`tan^-1sqrt((1 - cos x)/(1 + cos x)`

Find the derivatives of the following:

sin^-1 (3x – 4x³)