Find the derivatives of the following:y = xcosx - Mathematics

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

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g(t) = 4 sec t + tan t

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

y = (x² + 5) log(1 + x) e^–3x

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y = sin (e^x)

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

Differentiate the following:
y = sin²(cos kx)

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y = (1 + cos²)⁶

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