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:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = tan 3x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = sin (ex)
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
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 the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
