Advertisements
Advertisements
Question
Differentiate the following:
y = `"e"^(xcosx)`
Advertisements
Solution
y = `"e"^(xcosx)`
`("d"y)/("d"x) = "e"^(xcosx) (x - sinx + cosx * 1)`
`("d"y)/("d"x) = "e"^(xcosx) (cos x - x sin x)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
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 = (x2 + 5) log(1 + x) e–3x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
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:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
