Find the derivatives of the following: (cos x)log x

Find the derivatives of the following:

(cos x)^{log x}

बेरीज

y = (cos x)^{log x}

Taking log on both sides

log y = log (cos x)^{log x}

log y = (log x) log (cos x)

Differentiating with respect to x

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

`1/y ("d"y)/("d"x) = - tan x (log x) + (log(cosx))/x`

`("d"y)/("d"x) = y [(log(cos x))/x - tan x (log x)]`

`("d"y)/("d"x) = (cos x)^(logx) [(log(cos x))/x - tan x (log x)]`

shaalaa.com

Differentiation Rules

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

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 5 | पृष्ठ १७६

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 = tan θ (sin θ + cos θ)

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

y = log₁₀ x

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

Differentiate the following:
y = tan (cos x)

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

Find the derivatives of the following:

`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`

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:

If y = e^tan–1x, show that (1 + x²)y” + (2x – 1)y’ = 0

Find the derivatives of the following:

If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ