Advertisements
Advertisements
प्रश्न
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Advertisements
उत्तर
f(t) = `root(3)(1 + tan "t")`
f(t) = `(1 + tan "t")^(1/3)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`f"'"("t") = 1/3 (1 + tan "t")^(1/3 - 1) "d"/"dt" (1 + tan "t")`
= `1/3 (1 + tan "t")^(- 2/3) (0 + sec^2 "t")`
= `1/3 xx 1/(1 + tan "t")^(2/3) xx sec^2"t"`
= `(sec^2"t")/(3(1 + tan "t")^(2/3)`
`f"'"("t") = 1/2 sec^2"t" (1 + tan "t")^(- 2/3)`
APPEARS IN
संबंधित प्रश्न
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:
g(t) = 4 sec t + tan t
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 = e-x . log x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = sin3x + cos3x
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-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:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a 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:
The differential coefficient of `log_10 x` with respect to `log_x 10` 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?
