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

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)`

shaalaa.com

Differentiation Rules

Is there an error in this question or solution?

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:

y = cos x – 2 tan x

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

y = sin x⁰

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

Differentiate the following:
F(x) = (x³ + 4x)⁷

Differentiate the following:
y = e^–mx

Differentiate the following:

y = `x"e"^(-x^2)`

Differentiate the following:

y = `5^((-1)/x)`

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

Differentiate the following:
y = `"e"^(xcosx)`

Differentiate the following:

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

Find the derivatives of the following:
y = `x^(cosx)`

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

Find the derivatives of the following:

(cos x)^{log x}