Advertisements
Advertisements
Question
Differentiate the following:
y = tan (cos x)
Advertisements
Solution
y = tan (cos x)
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = sec^2(cos x) xx "d"/("d"x) (cos x)`
= sec2 (cos x) × – sin x
`("d"y)/("d"x)` = – sin x . sec2(cos x)
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/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Differentiate the following:
y = sin (ex)
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = (1 + cos2)6
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
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:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
If y = sin–1x then find y”
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
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:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
