Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Advertisements
उत्तर
Let y = `tan^-1 ((6x)/(1 - 9x^2))`
y = `tan^-1 ((2 xx 3x)/(1 - (3x)^2))` ........(1)
Put 3x = tan θ
(1) ⇒ y = `tan^-1 ((2 xx tan theta)/(1 - tan^2 theta))`
y = `tan^-1 (tan 2theta)`
y = 2θ
`("d"y)/("d"theta) = 2 xx 1` = 2 ........(2)
3x = tan θ
`3 ("d"x)/("d"theta) = sec^2theta`
`3 ("d"x)/("d"theta) = 1 + tan^2 theta`
`("d"x)/("d"theta) = 1/3 (1 + (3x)^2)`
`("d"x)/("d"theta) = 1/3 (1 + 9x^2)` .........(3)
Using equation (2) and (3) we have
`(("d"y)/("d"theta))/(("d"x)/("d"theta)) = 2/(1/3 (1 + 9x^2))`
`("d"y)/("d"x) = 6/(1 + 9x^2)`
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:
y = ex sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + 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
Differentiate the following:
y = tan 3x
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^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = sin2(cos kx)
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:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
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:
If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` 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?
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
