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

Differentiate the following:

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

Sum

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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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 9 | Page 163

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 = `sinx/(1 + cosx)`

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

y = cosec x . cot x

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

y = e^-x . log x

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

y = log₁₀ x

Differentiate the following:
y = cos (a³ + x³)

Differentiate the following:
y = sin²(cos kx)

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

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

Differentiate the following:

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

Find the derivatives of the following:

(cos x)^{log x}