Differentiate the following:y = 1+2tanx

Differentiate the following:
y = `sqrt(1 + 2tanx)`

Sum

y = `sqrt(1 + 2tanx)`

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

`("d"y)/("d"x) = 1/2(1 + 2 tan x)^(1/2 - 1) xx "d"/("d"x) (1 + 2 tan x)`

= `1/2 (1 + 2 tan x)^(- 1/2) xx (0 + 2 sec^2 x)`

= `1/(2(1 + 2 tan x)^(1/2)) xx 2sec^2x`

`("d"y)/("d"x) = (sec^2x)/sqrt(1 -+ 2 tanx)`

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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 21 | Page 163

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

y = `tan x/x`

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 = e^-x . log x

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

y = (x² + 5) log(1 + x) e^–3x

Differentiate the following:
y = (x² + 4x + 6)⁵

Differentiate the following:
y = e^–mx

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

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

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

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

Find the derivatives of the following:

`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`

Find the derivatives of the following:

x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`

Find the derivatives of the following:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`

Find the derivatives of the following:

If y = sin^–1x then find y”