Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Solution
y = u v
⇒ y’ = uv’ + vu’
u = cosec x
⇒ u’ = – cosec x cot x
v = cot x
⇒ v’ = – cosec2 x
`("d"y)/("d"x)` = (cosec x)(– cosec2x) + cot x(– coseç x cot x)
= cosec3x – cosec x cot2x
= – cosec x (cosec2x + cot2x)
= `- 1/sinx (1/(sin^2x)+ (cos^2x)/(sin^2x))`
= `- ((1 + cos^2x))/(sinx sin^2x)`
= `- ((1 + cos^2x))/(sin^x)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos 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 = x sin x cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = e–mx
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `5^((-1)/x)`
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
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 f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
