Find the derivatives of the following:tan (x + y) + tan (x – y) = x

Find the derivatives of the following:
tan (x + y) + tan (x – y) = x

Sum

tan (x + y) + tan (x – y) = x

Differentiating with respect to x

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

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

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

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

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [Page 176]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 8 | Page 176

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/(1 + cosx)`

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

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

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

Differentiate the following:
y = tan (cos x)

Differentiate the following:
y = sin³x + cos³x

Differentiate the following:
y = sin²(cos kx)

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

Find the derivatives of the following:

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

Find the derivatives of the following:

`cos^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:

Find the derivative of sin x² with respect to x²

Find the derivatives of the following:

Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`

Find the derivatives of the following:

If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x²)y₂ – 3xy₁ – y = 0