Find the derivatives of the following:xy = yx

Find the derivatives of the following:
x^y = y^x

योग

x^y = y^x

Taking log on both sides

log x^y = log y^x

y log x = x log y

Differentiate with respect to x

`y xx 1/x + (log x) ("d"y)/("d"x) = x * 1/y xx ("d"y)/("d"x) + (log y) 1`

`y/x + (log x) ("d"y)/("d"x) = x/y * ("d"y)/("d"x) + log y`

`(log ) ("d"y)/("d"x) - x/y ("d"y)/("d"x) = log y - y/x`

`(log x - x/y) ("d"y)/("d"x) = log y - y/x`

`(y log x - x)/y * ("d"y)/("d"x) = (x log y - y)/x`

`("d"y)/("d"x) = y/x * (x log y - y)/(y log x - x)`

`("d"y)/("d"x) = (y (x log y - y))/(x(y log x - x))`

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Differentiation Rules

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 4 | पृष्ठ १७६

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

f(x) = x sin x

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 = x sin x cos x

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

y = sin x⁰

Differentiate the following:
y = `root(3)(1 + x^3)`

Differentiate the following:
y = 4 sec 5x

Differentiate the following:
y = (2x – 5)⁴ (8x² – 5)^–3

Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`

Differentiate the following:
y = `sin(tan(sqrt(sinx)))`

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