Find the derivatives of the following functions with respect to corresponding independent variables: y = tan θ (sin θ + cos θ) - Mathematics

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

y = tan θ (sin θ + cos θ)

Sum

y = tan θ (sin θ + cos θ)

`("d"y)/("d"x)` = tan θ (cos θ – sin θ) + (sin θ + cos 0) sec² θ

= tan θ cos θ – tan θ sin θ + sin θ sec²θ + cos θ sec²θ

= `tan theta cos theta - tan theta sin theta + sintheta/(cos^2theta) + costheta/(cos^2theta)`

= `sin theta/cos theta cos theta - sin theta/cos theta sin theta + sin theta/cos theta * 1/cos theta + 1/costheta`

= sin θ – sin²θ sec θ + tan θ sec θ + sec θ

= sin θ + (1 – sin²θ) sec θ + sec θ tan θ

= `sin theta + cos^2theta xx 1/cos theta + sectheta tan theta`

= sin θ + cos θ + sec θ tan θ

shaalaa.com

Differentiation Rules

Is there an error in this question or solution?

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 13 | Page 160

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:

g(t) = t³ cos t

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

y = `tan x/x`

Differentiate the following:
y = e^–mx

Differentiate the following:
y = 4 sec 5x

Differentiate the following:

y = `(x^2 + 1) root(3)(x^2 + 2)`

Differentiate the following:
y = tan (cos x)

Differentiate the following:

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

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

Find the derivatives of the following:
(cos x)^{log x}