Find the derivatives of the following:y = xcosx

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

बेरीज

y = `x^(cosx)`

Taking log on both sides

log y = log x^{cos x}

log y = cos x log x

Differentiating with respect to x

`1/y * ("d"y)/("d"x) = cosx xx 1/x + (logx)(- sinx)`

`1/y * ("d"y)/("d"x) = 1/x cos x - sin x * log x`

`("d"y)/("d"x) = y[cosx/x - sin x * log x]`

`("d"y)/("d"x) = x^(cosx) [cosx/x - sin x log x]`

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Differentiation Rules

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

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 1 | पृष्ठ १७६

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 = e^x sin x

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

y = `(tanx - 1)/secx`

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

y = `sinx/x^2`

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

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

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

Differentiate the following:
y = e^–mx

Differentiate the following:

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

Differentiate the following:

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

Find the derivatives of the following:

(cos x)^{log x}