Advertisements
Advertisements
Question
Differentiate the following:
y = tan 3x
Advertisements
Solution
y = tan 3x
Put u = 3x
`("d"u)/("d"x)` = 3
Now y = tan u
⇒ `("d"y)/("d"x)` = sec2u
So `("d"y)/("d"x) = ("d"y)/("d"u) xx ("d"u)/("d"x)` = (sec2 u)(3)
= 3 sec2 3x
APPEARS IN
RELATED QUESTIONS
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) = 4 sec t + tan t
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 = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
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 = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = `"e"^(xcosx)`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
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 x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
Find the derivatives of the following:
If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
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 x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
