Advertisements
Advertisements
प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
Advertisements
उत्तर
y = `x/(sin x + cosx)`
`("d"y)/("d"x) = ((sinx + cosx)(1) - x(cosx - sinx))/(sinx + cos x)^2`
`("d"y)/("d"x) = ((sinx + cosx)- x(cosx - sinx))/(sinx + cos x)^2`
`("d"y)/("d"x) = (sinx + cosx - xcosx + xsinx)/(sinx + cosx)^2`
`("d"y)/("d"x) = ((1 + x) sinx + (1 - x)cosx)/(sinx + cosx)^2`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Differentiate the following:
y = tan 3x
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
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:
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:
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 y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
