Advertisements
Advertisements
Question
Find the derivatives of the following:
y = `x^(cosx)`
Advertisements
Solution
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
RELATED QUESTIONS
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 = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
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 = x sin x cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = sin (ex)
Differentiate the following:
y = e–mx
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
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:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Choose the correct alternative:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
