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 = sin x + cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
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
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Differentiate the following:
y = tan 3x
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = (1 + cos2)6
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – 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:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` 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?
