Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
y = `x^(cosx)`
Advertisements
उत्तर
y = `x^(cosx)`
Taking log on both sides
log y = log xcos 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]`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = tan 3x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
