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]`

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 1 | पृष्ठ १७६

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

f(x) = x – 3 sin 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 = `tan x/x`

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

y = log₁₀ x

Differentiate the following:
y = cos (tan x)

Differentiate the following:
y = e^–mx

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

Differentiate the following:

s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`

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

Find the derivatives of the following:

If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`

Find the derivatives of the following:

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

Find the derivatives of the following:

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

Find the derivatives of the following:

Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`

Find the derivatives of the following:

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