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 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan x
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
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 = `sinx/(1 + cosx)`
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:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^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))`
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:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
