Find the derivatives of the following functions with respect to corresponding independent variables: y = tanx-1secx

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

y = `(tanx - 1)/secx`

Sum

y = `(tanx - 1)/secx`

`("d"y)/("d"x) = (secx(sec^2x - 0) - (tan x - )secx tanx)/(sec x)^2`

`("d"y)/("d"x) = (secx[sec^2x - (tan x - 1) tanx])/(sec^2x)`

= `([sec^3x - tan^2xx + tanx])/secx`

= `((1 + tanx))/secx`

= `cos x (1 + sinx/cosx)`

`("d"y)/("d"x)` = cos x + sin x

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [Page 160]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 11 | Page 160

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 = x sin x cos 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 = `"e"^sqrt(x)`

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

Differentiate the following:

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

Differentiate the following:
y = 4 sec 5x

Differentiate the following:
y = tan (cos x)

Differentiate the following:

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

Find the derivatives of the following:

(cos x)^{log x}