Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Advertisements
उत्तर
y = `sqrt(1 + 2tanx)`
y = `(1 + 2 tan x)^(1/2)`
`("d"y)/("d"x) = 1/2(1 + 2 tan x)^(1/2 - 1) xx "d"/("d"x) (1 + 2 tan x)`
= `1/2 (1 + 2 tan x)^(- 1/2) xx (0 + 2 sec^2 x)`
= `1/(2(1 + 2 tan x)^(1/2)) xx 2sec^2x`
`("d"y)/("d"x) = (sec^2x)/sqrt(1 -+ 2 tanx)`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
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 = cos (tan x)
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `5^((-1)/x)`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
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^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
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 = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) 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) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
